MATH 111

Providing further information on functions and their graphs, including: 1. Identify intervals on which a function increases, decreases, or is constant. 2. Use graphs to locate relative maxima or minima. 3. Test for symmetry. 4. Identify even or odd functions and recognize their symmetries. 5. Understand and use piecewise functions. 6. Find and simplify a function's difference quotient.

Understanding linear functions and their slopes, including: 1. Calculate a line's slope. 2. Write the point-slope form of the equation of a line. 3. Write and graph the slope-intercept form of the equation of a line. 4. Graph horizontal or vertical lines. 5. Recognize and use the general form of a line's equation. 6. Use intercepts to graph a linear function in standard form. 7. Model data with linear functions and make predictions.

Provide in-depth information about slopes, including: 1. Find slopes and equations of parallel and perpendicular lines. 2. Interpret slope as rate of change. 3. Find a function's average rate of change.

Understanding combinations of functions and composite functions, including: 1. Find the domain of a function. 2. Combine functions using the algebra of functions, specifying domains. 3. Form composite functions. 4. Write functions as compositions.

Understanding the concept of inverse functions, including: 1. Verify inverse functions. 2. Find the inverse of a function. 3. Use the horizontal line test to determine if a function has an inverse function, also called "one-to-one". 4. Use the graph of a one-to-one function to graph its inverse function. 5. Find the inverse of a function and graph both functions on the same axes.

Calculating the distance of a circle using the distance and midpoint formulas, including: 1. Find the distance between two points. 2. Find the midpoint of a line segment. 3. Write the standard form of a circle's equation. 4. Give the center and radius of a circle whose equation is in standard form. 5. Convert the general form of a circle's equation to standard form.

Understanding the basics of functions and their graphs, including: 1. Find the domain and range of a relation. 2. Determine whether a relation is a function. 3. Determine whether an equation represents a function. 4. Evaluate a function. 5. Graph functions by plotting points. 6. Use the vertical line test to identify functions. 7. Obtain information about a function from its graph. 8. Identify the domain and range of a function from its graph. 9. Identify intercepts from a function's ...

Understand the basics of functions and their graphs, including: 1. Find the domain and range of a relation. 2. Determine whether a relation is a function. 3. Determine whether an equation represents a function. 4. Evaluate a function. 5. Graph functions by plotting points. 6. Use the vertical line test to identify functions. 7. Obtain information about a function from its graph. 8. Identify the domain and range of a function from its graph. 9. Identify intercepts from a function's gra...

Understanding the basics of functions and their graphs, including: 1. Finding the domain and range of a relation. 2. Determine whether a relation is a function. 3. Determine whether an equation represents a function. 4. Evaluate a function. 5. Graph functions by plotting points. 6. Use the vertical line test to identify functions. 7. Identify the domain and range of a function from its graph. 8. Identify intercepts from a function's graph. Further information on functions and thei...

Understanding the transformations of functions, including: 1. Recognize graphs of common functions. 2. Use the vertical shifts to graph functions. 3. Use horizontal shifts to graph functions. 4. Use reflections to graph functions. 5. Use vertical stretching and shrinking to graph functions. 6. Use horizontal stretching and shrinking to graph functions. 7. Graph functions involving a sequence of transformations.