Find inverse functions.

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write [...]

(+) Verify by composition that one function is the inverse of another.

(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.

(+) Produce an invertible function from a non-invertible function by restricting the domain.

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Distinguish between situations that can be modeled with linear functions and with exponential functions.*

Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over [...]

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*

Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric [...]

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) [...]

For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers [...]

Interpret the parameters in a linear or exponential function in terms of a context.*

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted [...]

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) [...]

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of [...]

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element [...]

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of [...]

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci [...]

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of [...]

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, [...]

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified [...]

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for [...]

Graph linear and quadratic functions and show intercepts, maxima, and minima.*

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.*

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.*

(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.*

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the [...]

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry [...]

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions [...]

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [...]

Write a function that describes a relationship between two quantities.*

Determine an explicit expression, a recursive process, or steps for calculation from a context.

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 [...]

(+) Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and [...]

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and [...]

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division [...]

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic [...]

Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph [...]

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable [...]

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s [...]

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, [...]

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve quadratic equations in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form [...]

Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and [...]