9-12.1.B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
9-12.1.C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
9-12.2 The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.
9-12.2.A graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b to the x power, f(x)=|x|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval;
9-12.2.C describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and
9-12.4 The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.
9-12.4.A write the quadratic function given three specified points in the plane;
9-12.4.B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;
9-12.4.G identify extraneous solutions of square root equations; and
9-12.4.H solve quadratic inequalities.
9-12.5 The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.
9-12.5.A determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d;
9-12.5.B formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;
9-12.5.D solve exponential equations of the form y = ab to the x power where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions; and
9-12.5.E determine the reasonableness of a solution to a logarithmic equation.
9-12.6 The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.
9-12.6.A analyze the effect on the graphs of f(x) = x³ and f(x) = ³√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d;