# Functions and equations

Here is a list of all of the skills that cover functions and equations! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Second-grade skills

- E.8 Addition input/output tables - sums to 20
- F.9 Subtraction input/output tables - up to 18
- G.7 Addition input/output tables - up to two digits
- H.7 Subtraction input/output tables - up to two digits
- I.4 Addition input/output tables - up to three digits
- J.4 Subtraction input/output tables - up to three digits
- L.6 Input/output tables - write the rule - up to 20
- L.12 Input/output tables - write the rule - up to 100

## Third-grade skills

- C.2 Addition input/output tables - up to three digits
- C.10 Addition input/output tables - four or more digits
- D.2 Subtraction input/output tables - up to three digits
- D.8 Subtraction input/output tables - four or more digits
- H.4 Multiplication input/output tables
- L.3 Division input/output tables
- O.1 Identify equations
- O.2 Solve for the variable: addition and subtraction
- O.3 Solve for the variable: multiplication and division
- O.4 Solve for the variable: addition, subtraction, multiplication, and division
- O.5 Write variable equations to represent word problems

## Fourth-grade skills

- D.30 Multiplication input/output tables
- G.4 Write variable equations to represent word problems
- G.5 Solve variable equations
- H.1 Input/output tables with addition, subtraction, multiplication, and division
- H.2 Complete a table for a two-variable relationship
- H.3 Write a two-variable equation
- H.4 Graph a two-variable relationship

## Fifth-grade skills

- C.22 Multiplication input/output tables
- M.11 Multiply fractions by whole numbers: input/output tables
- V.4 Write variable equations: word problems
- V.5 Solve equations with whole numbers
- V.6 Solve equations with decimals
- V.7 Find a value using two-variable equations
- V.8 Complete a table for a two-variable relationship
- V.9 Complete a table from a graph
- V.10 Graph a two-variable relationship
- V.11 Write a two-variable equation

## Sixth-grade skills

- N.6 Add and subtract integers: input/output tables
- Z.1 Does x satisfy an equation?
- Z.2 Which x satisfies an equation?
- Z.3 Write an equation from words
- Z.4 Model and solve equations using algebra tiles
- Z.5 Write and solve equations that represent diagrams
- Z.6 Solve one-step equations with whole numbers
- Z.7 Solve one-step equations with decimals, fractions, and mixed numbers
- Z.8 Solve one-step equations: word problems
- Z.9 Solve two-step equations
- Z.10 Solve equations involving like terms
- Z.11 Solve equations involving integers
- BB.1 Does (x, y) satisfy an equation?
- BB.2 Identify independent and dependent variables
- BB.3 Find a value using two-variable equations
- BB.4 Solve word problems involving two-variable equations
- BB.5 Complete a table for a two-variable relationship
- BB.6 Write a two-variable equation
- BB.7 Identify the graph of an equation
- BB.8 Graph a two-variable equation
- BB.9 Interpret a graph: word problems
- BB.10 Write an equation from a graph using a table

## Seventh-grade skills

- K.2 Write equations for proportional relationships from tables
- K.5 Write equations for proportional relationships from graphs
- K.6 Identify proportional relationships
- K.8 Write and solve equations for proportional relationships
- R.11 Solve equations using properties
- S.1 Which x satisfies an equation?
- S.2 Write an equation from words
- S.3 Model and solve equations using algebra tiles
- S.4 Write and solve equations that represent diagrams
- S.5 Solve one-step equations
- S.6 Solve two-step equations
- S.7 Solve equations: word problems
- S.8 Solve equations involving like terms
- S.9 Solve equations: complete the solution
- U.1 Does (x, y) satisfy the equation?
- U.2 Identify independent and dependent variables
- U.3 Find a value using two-variable equations
- U.4 Solve word problems involving two-variable equations
- U.5 Complete a table for a two-variable relationship
- U.6 Write a two-variable equation
- U.7 Identify the graph of an equation
- U.8 Graph a two-variable equation
- U.9 Interpret a graph: word problems
- U.10 Write an equation from a graph using a table
- V.1 Find the slope from a graph
- V.2 Find the slope from two points
- V.4 Find the slope from an equation
- V.5 Graph a line using slope
- V.6 Write a linear function
- V.7 Identify linear and nonlinear functions

## Eighth-grade skills

- F.18 Solve equations involving squares and square roots
- F.20 Solve equations involving cubes and cube roots
- I.2 Write equations for proportional relationships from tables
- I.5 Write equations for proportional relationships from graphs
- I.6 Identify proportional relationships
- I.9 Write and solve equations for proportional relationships
- W.1 Which x satisfies an equation?
- W.2 Write an equation from words
- W.3 Model and solve equations using algebra tiles
- W.4 Write and solve equations that represent diagrams
- W.6 Solve one-step equations
- W.7 Solve two-step equations
- W.8 Solve multi-step equations
- W.9 Solve equations involving like terms
- W.10 Solve equations with variables on both sides
- W.11 Solve equations: mixed review
- W.12 Solve equations: complete the solution
- W.13 Solve equations: word problems
- W.14 Find the number of solutions
- Y.1 Find the slope of a graph
- Y.2 Find the slope from two points
- Y.4 Find the slope of a linear equation
- Y.5 Graph a line using slope
- Y.6 Graph a line from an equation in slope-intercept form
- Y.7 Write a linear equation from a slope and y-intercept
- Y.8 Write a linear equation from a graph
- Y.9 Write a linear equation from a slope and a point
- Y.10 Write a linear equation from two points
- Y.11 Convert a linear equation in standard form to slope-intercept form
- Y.12 Graph a line from an equation in standard form
- Y.13 Slopes of parallel and perpendicular lines
- Z.1 Identify functions
- Z.2 Does (x, y) satisfy the linear function?
- Z.3 Identify independent and dependent variables
- Z.6 Evaluate a linear function
- Z.7 Complete a table for a linear function
- Z.8 Complete a table and graph a linear function
- Z.9 Interpret the graph of a linear function: word problems
- Z.10 Write a linear function from a table
- Z.11 Compare linear functions: graphs, tables, and equations
- Z.12 Write linear functions: word problems
- Z.13 Interpret linear functions
- Z.14 Identify linear and nonlinear functions
- Z.15 Does (x, y) satisfy the nonlinear function?
- Z.16 Evaluate a nonlinear function
- Z.17 Find values using function graphs
- Z.18 Complete a table for a function graph
- AA.1 Is (x, y) a solution to the system of equations?
- AA.2 Solve a system of equations by graphing
- AA.3 Solve a system of equations by graphing: word problems
- AA.4 Find the number of solutions to a system of equations by graphing
- AA.5 Find the number of solutions to a system of equations
- AA.6 Classify a system of equations by graphing
- AA.7 Classify a system of equations
- AA.8 Solve a system of equations using substitution
- AA.9 Solve a system of equations using substitution: word problems
- AA.10 Solve a system of equations using elimination
- AA.11 Solve a system of equations using elimination: word problems
- DD.9 Scatter plots: line of best fit

## Algebra 1 skills

- I.4 Write variable equations
- I.5 Does x satisfy the equation?
- I.6 Which x satisfies an equation?
- I.7 Solve equations using order of operations
- J.1 Model and solve equations using algebra tiles
- J.2 Write and solve equations that represent diagrams
- J.3 Solve one-step linear equations
- J.4 Solve two-step linear equations
- J.5 Solve advanced linear equations
- J.6 Solve equations with variables on both sides
- J.7 Solve equations: complete the solution
- J.8 Find the number of solutions
- J.10 Solve linear equations: word problems
- J.11 Solve linear equations: mixed review
- L.1 Solve absolute value equations
- L.2 Graph solutions to absolute value equations
- L.3 Solve absolute value inequalities
- L.4 Graph solutions to absolute value inequalities
- O.4 Rate of travel: word problems
- O.5 Weighted averages: word problems
- Q.1 Relations: convert between tables, graphs, mappings, and lists of points
- Q.2 Domain and range of relations
- Q.3 Identify independent and dependent variables
- Q.4 Identify functions
- Q.5 Identify functions: vertical line test
- Q.6 Find values using function graphs
- Q.7 Evaluate a function
- Q.8 Evaluate a function: plug in an expression
- Q.9 Complete a function table from a graph
- Q.10 Complete a function table from an equation
- Q.11 Interpret the graph of a function: word problems
- R.1 Identify proportional relationships
- R.2 Find the constant of variation
- R.3 Graph a proportional relationship
- R.4 Write direct variation equations
- R.5 Write and solve direct variation equations
- R.6 Identify direct variation and inverse variation
- R.7 Write inverse variation equations
- R.8 Write and solve inverse variation equations
- S.1 Identify linear functions
- S.2 Find the slope of a graph
- S.3 Find the slope from two points
- S.5 Slope-intercept form: find the slope and y-intercept
- S.6 Slope-intercept form: graph an equation
- S.7 Slope-intercept form: write an equation from a graph
- S.8 Slope-intercept form: write an equation
- S.9 Slope-intercept form: write an equation from a table
- S.10 Slope-intercept form: write an equation from a word problem
- S.11 Linear equations: solve for y
- S.12 Write linear functions to solve word problems
- S.13 Complete a table and graph a linear function
- S.14 Compare linear functions: graphs, tables, and equations
- S.15 Write equations in standard form
- S.16 Standard form: find x- and y-intercepts
- S.17 Standard form: graph an equation
- S.18 Equations of horizontal and vertical lines
- S.19 Graph a horizontal or vertical line
- S.20 Point-slope form: graph an equation
- S.21 Point-slope form: write an equation
- S.22 Point-slope form: write an equation from a graph
- S.23 Slopes of parallel and perpendicular lines
- S.24 Write an equation for a parallel or perpendicular line
- S.25 Transformations of linear functions
- U.1 Is (x, y) a solution to the system of equations?
- U.2 Solve a system of equations by graphing
- U.3 Solve a system of equations by graphing: word problems
- U.4 Find the number of solutions to a system of equations by graphing
- U.5 Find the number of solutions to a system of equations
- U.6 Classify a system of equations by graphing
- U.7 Classify a system of equations
- U.8 Solve a system of equations using substitution
- U.9 Solve a system of equations using substitution: word problems
- U.10 Solve a system of equations using elimination
- U.11 Solve a system of equations using elimination: word problems
- U.12 Solve a system of equations using augmented matrices
- U.13 Solve a system of equations using augmented matrices: word problems
- U.14 Solve a system of equations using any method
- U.15 Solve a system of equations using any method: word problems
- X.1 Evaluate an exponential function
- X.2 Match exponential functions and graphs
- X.3 Domain and range of exponential functions: graphs
- X.4 Domain and range of exponential functions: equations
- BB.1 Characteristics of quadratic functions
- BB.2 Complete a function table: quadratic functions
- BB.3 Transformations of quadratic functions
- BB.4 Graph quadratic functions in vertex form
- BB.5 Solve a quadratic equation using square roots
- BB.6 Solve a quadratic equation using the zero product property
- BB.7 Solve a quadratic equation by factoring
- BB.9 Solve a quadratic equation by completing the square
- BB.10 Solve a quadratic equation using the quadratic formula
- BB.11 Using the discriminant
- BB.12 Match quadratic functions and graphs
- BB.13 Systems of linear and quadratic equations
- CC.1 Identify linear, quadratic, and exponential functions from graphs
- CC.2 Identify linear, quadratic, and exponential functions from tables
- CC.3 Write linear, quadratic, and exponential functions
- CC.4 Linear functions over unit intervals
- CC.5 Exponential functions over unit intervals
- CC.6 Describe linear and exponential growth and decay
- DD.1 Complete a function table: absolute value functions
- DD.2 Graph an absolute value function
- DD.3 Domain and range of absolute value functions: graphs
- DD.4 Domain and range of absolute value functions: equations
- DD.5 Transformations of absolute value functions
- FF.1 Evaluate a radical function
- FF.2 Domain and range of radical functions: graphs
- FF.3 Domain and range of radical functions: equations
- FF.4 Solve radical equations I
- FF.5 Solve radical equations II
- GG.1 Rational functions: asymptotes and excluded values
- GG.7 Solve rational equations
- KK.12 Scatter plots: line of best fit
- KK.13 Find the equation of a regression line

## Geometry skills

- A.5 Write variable expressions
- A.6 Solve linear equations
- A.8 Solve systems of linear equations
- A.9 Solve a quadratic equation by factoring
- A.10 Solve a quadratic equation using the quadratic formula
- E.3 Graph a linear equation
- E.4 Equations of lines
- E.5 Slopes of parallel and perpendicular lines
- E.6 Equations of parallel and perpendicular lines

## Algebra 2 skills

- B.1 Solve linear equations
- B.2 Solve linear equations: word problems
- B.3 Solve equations: complete the solution
- B.4 Solve absolute value equations
- B.5 Graph solutions to absolute value equations
- C.7 Graph solutions to absolute value inequalities
- D.1 Domain and range
- D.2 Identify functions
- D.3 Evaluate functions
- D.4 Find values using function graphs
- D.5 Complete a table for a function graph
- D.6 Find the slope of a linear function
- D.7 Graph a linear function
- D.8 Write the equation of a linear function
- D.9 Linear functions over unit intervals
- D.10 Average rate of change
- E.1 Is (x, y) a solution to the system of equations?
- E.2 Solve a system of equations by graphing
- E.3 Solve a system of equations by graphing: word problems
- E.7 Solve a system of equations using substitution: word problems
- E.8 Solve a system of equations using elimination
- E.9 Solve a system of equations using elimination: word problems
- E.10 Solve a system of equations using any method
- E.11 Solve a system of equations using any method: word problems
- E.12 Solve a system of equations in three variables using substitution
- E.13 Solve a system of equations in three variables using elimination
- E.14 Determine the number of solutions to a system of equations in three variables
- E.15 Solve a system of linear and quadratic equations
- E.16 Solve a non-linear system of equations
- G.18 Solve a system of equations using augmented matrices
- G.19 Solve a system of equations using augmented matrices: word problems
- J.1 Characteristics of quadratic functions
- J.2 Complete a function table: quadratic functions
- J.3 Graph a quadratic function
- J.4 Solve a quadratic equation using square roots
- J.5 Solve a quadratic equation using the zero product property
- J.6 Solve a quadratic equation by factoring
- J.7 Complete the square
- J.8 Solve a quadratic equation by completing the square
- J.9 Solve a quadratic equation using the quadratic formula
- J.10 Using the discriminant
- J.11 Match quadratic functions and graphs
- J.12 Write a quadratic function from its zeros
- K.7 Solve polynomial equations
- K.14 Match polynomials and graphs
- L.12 Domain and range of radical functions
- L.13 Solve radical equations
- N.1 Rational functions: asymptotes and excluded values
- N.7 Solve rational equations
- O.1 Add and subtract functions
- O.2 Multiply functions
- O.3 Divide functions
- O.4 Composition of linear functions: find a value
- O.5 Composition of linear functions: find an equation
- O.6 Composition of linear and quadratic functions: find a value
- O.7 Composition of linear and quadratic functions: find an equation
- O.8 Identify inverse functions
- O.9 Find values of inverse functions from tables
- O.10 Find values of inverse functions from graphs
- O.11 Find inverse functions and relations
- P.1 Function transformation rules
- P.2 Translations of functions
- P.3 Reflections of functions
- P.4 Dilations of functions
- P.5 Transformations of functions
- P.6 Describe function transformations
- S.9 Exponential functions over unit intervals
- S.11 Describe linear and exponential growth and decay
- Z.1 Find properties of sine functions
- Z.5 Find properties of cosine functions
- AA.1 Complementary angle identities
- AA.2 Symmetry and periodicity of trigonometric functions
- AA.3 Trigonometric identities I
- AA.4 Trigonometric identities II
- EE.6 Find the equation of a regression line

## Precalculus skills

- A.1 Domain and range
- A.2 Identify functions
- A.3 Evaluate functions
- A.4 Find values using function graphs
- A.5 Complete a table for a function graph
- A.6 Find the slope of a linear function
- A.7 Graph a linear function
- A.8 Write the equation of a linear function
- A.9 Linear functions over unit intervals
- A.10 Average rate of change
- A.11 Add, subtract, multiply, and divide functions
- A.12 Composition of functions
- A.13 Identify inverse functions
- A.14 Find values of inverse functions from tables
- A.15 Find values of inverse functions from graphs
- A.16 Find inverse functions and relations
- B.1 Function transformation rules
- B.2 Translations of functions
- B.3 Reflections of functions
- B.4 Dilations of functions
- B.5 Transformations of functions
- B.6 Describe function transformations
- C.1 Find the maximum or minimum value of a quadratic function
- C.2 Characteristics of quadratic functions
- C.3 Graph a quadratic function
- C.4 Match quadratic functions and graphs
- C.5 Solve a quadratic equation using square roots
- C.6 Solve a quadratic equation by factoring
- C.7 Solve a quadratic equation by completing the square
- C.8 Solve a quadratic equation using the quadratic formula
- C.9 Using the discriminant
- D.11 Match polynomials and graphs
- D.13 Solve equations with sums and differences of cubes
- D.15 Solve equations using a quadratic pattern
- E.1 Rational functions: asymptotes and excluded values
- E.2 Solve rational equations
- E.3 Check whether two rational functions are inverses
- F.13 Exponential functions over unit intervals
- F.15 Describe linear and exponential growth and decay
- G.1 Domain and range of radical functions
- G.2 Solve radical equations
- I.1 Solve a system of equations by graphing
- I.2 Solve a system of equations by graphing: word problems
- I.3 Classify a system of equations
- I.4 Solve a system of equations using substitution
- I.5 Solve a system of equations using substitution: word problems
- I.6 Solve a system of equations using elimination
- I.7 Solve a system of equations using elimination: word problems
- I.8 Solve a system of equations in three variables using substitution
- I.9 Solve a system of equations in three variables using elimination
- I.10 Determine the number of solutions to a system of equations in three variables
- N.1 Find properties of sine functions
- N.5 Find properties of cosine functions
- O.1 Complementary angle identities
- O.2 Symmetry and periodicity of trigonometric functions
- O.3 Trigonometric identities I
- O.4 Trigonometric identities II
- Z.8 Find the equation of a regression line

## Calculus skills

- A.1 Find values of functions from graphs
- A.2 Add, subtract, multiply, and divide functions
- A.3 Composition of functions
- A.4 Identify inverse functions
- A.5 Find values of inverse functions from tables
- A.6 Find values of inverse functions from graphs
- A.7 Find inverse functions and relations
- B.1 Function transformation rules
- B.2 Translations of functions
- B.3 Reflections of functions
- B.4 Dilations of functions
- B.5 Transformations of functions
- B.6 Describe function transformations
- C.8 Find properties of sine functions
- C.12 Find properties of cosine functions
- D.9 Describe linear and exponential growth and decay
- E.1 Find limits using graphs
- E.2 Find one-sided limits using graphs
- E.3 Determine if a limit exists
- F.1 Find limits using addition, subtraction, and multiplication laws
- F.2 Find limits using the division law
- F.3 Find limits using power and root laws
- F.4 Find limits using limit laws
- F.5 Find limits of polynomials and rational functions
- F.6 Find limits involving factorization and rationalization
- F.7 Find limits involving absolute value functions
- F.8 Find limits involving trigonometric functions
- G.1 Find limits at vertical asymptotes using graphs
- G.2 Determine end behavior using graphs
- G.3 Determine end behavior of polynomial and rational functions
- H.1 Find the limit at a vertical asymptote of a rational function I
- H.2 Find the limit at a vertical asymptote of a rational function II
- I.1 Identify graphs of continuous functions
- I.2 Determine continuity using graphs
- I.3 Determine one-sided continuity using graphs
- I.4 Find and analyze points of discontinuity using graphs
- I.5 Determine continuity on an interval using graphs
- I.6 Determine the continuity of a piecewise function at a point
- I.7 Make a piecewise function continuous
- I.8 Intermediate Value Theorem
- J.1 Average rate of change I
- J.2 Average rate of change II
- J.3 Find instantaneous rates of change
- J.4 Velocity as a rate of change
- J.5 Find values of derivatives using limits
- J.6 Find the slope of a tangent line using limits
- J.7 Find equations of tangent lines using limits
- K.1 Sum and difference rules
- K.2 Product rule
- K.3 Quotient rule
- K.4 Power rule I
- K.5 Power rule II
- K.6 Chain rule
- K.7 Inverse function rule
- L.1 Find derivatives of polynomials
- L.2 Find derivatives of rational functions
- L.3 Find derivatives of trigonometric functions I
- L.4 Find derivatives of trigonometric functions II
- L.5 Find derivatives of exponential functions
- L.6 Find derivatives of logarithmic functions
- L.7 Find derivatives of inverse trigonometric functions
- L.8 Find derivatives of radical functions
- L.9 Find derivatives using the product rule I
- L.10 Find derivatives using the product rule II
- L.11 Find derivatives using the quotient rule I
- L.12 Find derivatives using the quotient rule II
- L.13 Find derivatives using the chain rule I
- L.14 Find derivatives using the chain rule II
- M.1 Find derivatives using implicit differentiation
- M.2 Find tangent lines using implicit differentiation
- M.3 Find derivatives using logarithmic differentiation
- N.1 Find higher derivatives of polynomials
- N.2 Find higher derivatives of rational and radical functions
- N.3 Find second derivatives of trigonometric, exponential, and logarithmic functions
- N.4 Find higher derivatives using patterns