# Functions and equations

See recommended skills!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 view a sample question. 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.7Addition input/output tables - sums to 20
- F.8Subtraction input/output tables - up to 18
- G.7Addition input/output tables - up to two digits
- H.7Subtraction input/output tables - up to two digits
- I.4Addition input/output tables - up to three digits
- J.4Subtraction input/output tables - up to three digits
- L.6Input/output tables - write the rule - up to 20
- L.11Input/output tables - write the rule - up to 100

## Third-grade skills

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

## Fourth-grade skills

- D.29Multiplication input/output tables
- G.4Write variable equations to represent word problems
- G.5Solve variable equations
- H.1Input/output tables with addition, subtraction, multiplication, and division
- H.2Complete a table for a two-variable relationship
- H.3Write a two-variable equation
- H.4Graph a two-variable relationship

## Fifth-grade skills

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

## Sixth-grade skills

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

## Seventh-grade skills

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

## Eighth-grade skills

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

## Algebra 1 skills

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

## Geometry skills

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

## Algebra 2 skills

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

## Precalculus skills

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

## Calculus skills

- A.1Find values of functions from graphs
- A.2Add, subtract, multiply, and divide functions
- A.3Composition of functions
- A.4Identify inverse functions
- A.5Find values of inverse functions from tables
- A.6Find values of inverse functions from graphs
- A.7Find inverse functions and relations
- B.1Function transformation rules
- B.2Translations of functions
- B.3Reflections of functions
- B.4Dilations of functions
- B.5Transformations of functions
- B.6Describe function transformations
- C.8Find properties of sine functions
- C.12Find properties of cosine functions
- D.9Describe linear and exponential growth and decay
- E.1Find limits using graphs
- E.2Find one-sided limits using graphs
- E.3Determine if a limit exists
- F.1Find limits using addition, subtraction, and multiplication laws
- F.2Find limits using the division law
- F.3Find limits using power and root laws
- F.4Find limits using limit laws
- F.5Find limits of polynomials and rational functions
- F.6Find limits involving factorization and rationalization
- G.1Find limits at vertical asymptotes using graphs
- G.2Determine end behavior using graphs
- G.3Determine end behavior of polynomial and rational functions
- H.1Find the limit at a vertical asymptote of a rational function I
- H.2Find the limit at a vertical asymptote of a rational function II
- I.1Identify graphs of continuous functions
- I.2Determine continuity using graphs
- I.3Determine one-sided continuity using graphs
- I.4Find and analyze points of discontinuity using graphs
- I.5Determine continuity on an interval using graphs
- I.6Determine the continuity of a piecewise defined function at a point
- I.7Intermediate Value Theorem
- J.1Average rate of change I
- J.2Average rate of change II
- J.3Find instantaneous rates of change
- J.4Velocity as a rate of change
- J.5Find values of derivatives using limits
- J.6Find the slope of a tangent line using limits
- J.7Find equations of tangent lines using limits
- K.1Sum and difference rules
- K.2Product rule
- K.3Quotient rule
- K.4Power rule I
- K.5Power rule II
- K.6Find derivatives of polynomials
- K.7Find derivatives of rational functions
- K.8Find derivatives of trigonometric functions
- K.9Chain rule
- K.10Find derivatives using implicit differentiation
- K.11Find tangent lines using implicit differentiation
- K.12Find derivatives of exponential functions
- K.13Find derivatives of logarithmic functions
- K.14Find derivatives using the product rule I
- K.15Find derivatives using the product rule II
- K.16Find derivatives using the quotient rule I
- K.17Find derivatives using the quotient rule II