Graphs and Functions

Graphs of Equations (3 topics)

• Finding intercepts of a nonlinear function given its graph
• Finding x- and y-intercepts of the graph of a nonlinear equation
• Determining if graphs have symmetry with respect to the x-axis, y-axis, or origin

Slope and Equations of Lines (3 topics)

• Writing an equation in slope-intercept form given the slope and a point
• Writing the equation of the line through two given points
• Writing equations of lines parallel and perpendicular to a given line through a point

Linear Applications (2 topics)

• Writing and evaluating a function that models a real-world situation - Advanced
• Writing an equation and drawing its graph to model a real-world situation - Advanced

Review of Systems of Linear Equations (1 topic)

• Solving a system of linear equations using elimination with multiplication and addition

Functions (9 topics)

• Vertical line test
• Evaluating functions - Absolute value, rational, radical
• Evaluating a piecewise-defined function
• Variable expressions as inputs of functions - Problem type 3
• Domain of a rational function - Excluded values
• Domain of a rational function - Interval notation
• Determining whether an equation defines a function - Advanced
• Finding a difference quotient for a linear or quadratic function
• Finding a difference quotient for a rational function

Graphs of Functions (17 topics)

• Finding inputs and outputs of a function from its graph
• Domain and range from the graph of a piecewise function
• Finding where a function is increasing, decreasing, or constant given the graph - Interval notation
• Finding local maxima and minima of a function given the graph
• Finding the absolute maximum and minimum of a function given the graph
• Finding values and intervals where the graph of a function is zero, positive, or negative
• Graphing a function of the form f of x equals ax-squared
• Graphing a function of the form f of x equals ax-squared plus c
• Graphing a parabola of the form y equals x minus h squared plus k
• Graphing a square root function - Problem type 2
• Matching parent graphs with their equations
• Graphing a piecewise-defined function - Problem type 3
• Even and odd functions - Problem type 1
• Even and odd functions - Problem type 2
• Finding the average rate of change of a function
• Finding the average rate of change of a function given its graph
• Word problem involving average rate of change

Transformations (7 topics)

• Translating the graph of a parabola - Two steps
• How the leading coefficient affects the shape of a parabola
• Writing an equation for a function after a vertical translation
• Translating the graph of a function - Two steps
• Transforming the graph of a function by reflecting over an axis
• Transforming the graph of a function by shrinking or stretching
• Writing an equation for a function after a vertical and horizontal translation

Combining Functions; Composite Functions; Inverse Functions (13 topics)

• Sum, difference, and product of two functions
• Quotient of two functions - Advanced
• Combining functions - Advanced
• Composition of two functions - Basic
• Expressing a function as a composition of two functions
• Composition of two functions - Advanced
• Composition of two rational functions
• Horizontal line test
• Determining whether two functions are inverses of each other
• Inverse functions - Quadratic, square root
• Inverse functions - Cubic, cube root
• Inverse functions - Rational
• Graphing the inverse of a function given its graph