- Recognize a single-variable equation as linear and solve it (0, 1, or inf. many soln's).
- Translate a problem situation into an equation and solve.
- Write inequalities corresponding to problem situations.
- Write an interval using inequalities and graph it.
- Solve linear inequalities.
- Solve application problems involving linear inequalities.
- Solve absolute value equations.
- Solve absolute value inequalities.
- Identify and simplify complex numbers.
- Add, subtract, multiply, and divide complex numbers.
- Simplify powers of .
- Solve quadratic equations by factoring.
- Solve quadratic equations by using square roots.
- Solve quadratic equations by using the quadratic formula.
- Determine the values of the variable that are restricted from a rational expression.
- Solve rational equations that reduce to linear or quadratic.
- Solve equations using odd roots.
- Solve radical equations.
- Solve equations involving rational exponents.
- Solve equations that are quadratic in form.

- Graph two-variable equations in the rectangular coordinate system.
- Find the distance between two points in the rectangular coordinate system.
- Determine the midpoint of two points.
- Use the standard form equation of a circle.
- Graph circles.
- Gain and demonstrate familiarity with some basic graphs.
- Determine solutions of two-variable linear equations.
- Graph a line by finding two points on the line.
- Find the - and -intercepts of a line.
- Compute the slope of a line and interpret it as a rate of change.
- Identify equations of horizontal or vertical lines and graph them.
- Determine lines parallel or perpendicular to given lines.
- Find and apply the slope-intercept form of the equation of a line.
- Find and apply the point-slope form of the equation of a line.
- Graph a line using its slope and a point.
- Find lines parallel or perpendicular to given lines.
- Apply lines and linear equations in real-world applications.
- Determine whether a relation is a function.
- Determine the domain and range of a function.
- Use function notation and evaluate functions.
- Interpret graphs of functions.
- Evaluate difference quotients.
- Given the graph of a function, determine where the function is positive, negative, or zero.
- Given the graph of a function, determine intervals on which the function is increasing, decreasing, or constant.
- Given the graph of a function, determine the local maxima and minima.
- Determine if a graph has symmetry.

- Develop and demonstrate a familiarity with the graphs of basic functions (Toolbox Functions).
- Apply the transformations (shifts, reflections, stretches, and compressions) to basic graphs to obtain more general graphs.
- Determine the transformations that result in a given graph.
- Develop a familiarity with the whole-number power functions and basic rational functions.
- Apply transformations to basic functions.
- Define and evaluate piecewise functions.
- Sketch the graph of a piecewise-defined function.
- Compute sums, differences, products, and quotients of functions.
- Compute a composition of functions.
- Write a function as a composition of functions.
- Solve problems involving operations on functions.

- Find the vertex, intercepts, and symmetry axis of a parabola.
- Write a quadratic function in vertex form.
- Find the equation of a quadratic function from its graph.
- Solve application problems involving quadratic functions and parabolas.
- Find the zeros of a polynomial and determine their multiplicities.
- Carry out polynomial long division and synthetic division.
- Apply the remainder and factor theorems.
- Apply the Fundamental Theorem of Algebra.
- Use common tests to determine the nature of a polynomial's zeros.
- Factor a polynomial with real coefficients into a product of linear factors and irreducible quadratic factors.
- Determine the end behavior of a polynomial function.
- Use multiplicities of zeros and end behavior to graph a polynomial function.
- Determine the domain of a rational function.
- Determine the vertical, horizontal, and/or slant asymptotes of the graph of a rational function.
- Sketch the graph of a rational function.
- Solve polynomial inequalities.
- Solve rational inequalities.

*Last updated April 28, 2020*