Functions and Lines

Functions and Lines (56 topics)

Tables and Graphs of Lines (9 topics)

• Table for a linear equation
• Identifying solutions to a linear equation in two variables
• Graphing a linear equation of the form y = mx
• Graphing a line given its equation in slope-intercept form - Integer slope
• Graphing a line given its equation in slope-intercept form - Fractional slope
• Graphing a line given its equation in standard form
• Graphing a vertical or horizontal line
• Finding x- and y-intercepts given the graph of a line on a grid
• Graphing a line given its x- and y-intercepts

Slope (3 topics)

• Classifying slopes given graphs of lines
• Finding slope given the graph of a line on a grid
• Finding slope given two points on the line

Direct Variation (2 topics)

• Identifying direct variation equations
• Identifying direct variation from ordered pairs and writing equations

Equations of Lines (6 topics)

• Finding the slope and y-intercept of a line given its equation in the form Ax plus By = C
• Graphing a line by first finding its slope and y-intercept
• Writing an equation and graphing a line given its slope and y-intercept
• Writing an equation in slope-intercept form given the slope and a point
• Writing an equation of a line given the y-intercept and another point
• Writing the equation of the line through two given points

Applications of Linear Equations with Two Variables (4 topics)

• Writing and evaluating a function that models a real-world situation - Advanced
• Comparing properties of linear functions given in different forms
• Application problem with a linear function - Finding a coordinate given the slope and a point
• Application problem with a linear function - Finding a coordinate given two points

Scatter Plots and Lines of Best Fit (4 topics)

• Scatter plots and correlation
• Approximating the equation of a line of best fit and making predictions
• Computing residuals
• Linear relationship and the correlation coefficient

Introduction to Functions (6 topics)

• Identifying functions from relations
• Vertical line test
• Domain and range from ordered pairs
• Table for a linear function
• Evaluating functions - Linear and quadratic or cubic
• Domain and range of a linear function that models a real-world situation

Arithmetic Sequences (6 topics)

• Finding the first terms of a sequence using a recursive rule
• Identifying arithmetic sequences and finding the common difference
• Finding a specified term of an arithmetic sequence given the first terms
• Finding a specified term of an arithmetic sequence given the common difference and first term
• Writing an explicit rule for an arithmetic sequence
• Writing a recursive rule for an arithmetic sequence

Graphs of Functions (9 topics)

• Finding where a function is increasing, decreasing, or constant given the graph
• Finding local maxima and minima of a function given the graph
• Choosing a graph to fit a narrative - Advanced
• Graphing an absolute value equation of the form y = A times abs x
• Graphing an absolute value equation in the plane - Basic
• Graphing an absolute value equation in the plane - Advanced
• Graphing a parabola of the form y equals ax2
• Graphing a parabola of the form y equals ax2 plus c
• Graphing a parabola of the form y equals x minus h squared plus k

Transformations (7 topics)

• Translating the graph of a parabola - One step
• How the leading coefficient affects the shape of a parabola
• Translating the graph of an absolute value function - One step
• Translating the graph of an absolute value function - Two steps
• How the leading coefficient affects the graph of an absolute value function
• Writing an equation for a function after a vertical translation
• Writing an equation for a function after a vertical and horizontal translation