# Math 1021 College Algebra Topics

## Math 1021 Pages

Linear Equations

• Recognizing linear equations
• Solving linear equations with integer coefficients
• Solving linear equations involving fractions
• Solving linear equations involving decimals
• Recognizing rational equations
• Solving rational equations that lead to linear equations

• Solving quadratic equations by factoring and the zero product property
• Solving quadratic equations using the square root property
• Using the discriminant to determine the type of solutions of a quadratic equation

Other Types of Equations

• Solving higher-order polynomial equations
• Solving equations that are quadratic in form
• Solving equations involving single radicals

Linear Inequalities

• Solving linear inequalities
• Solving three-part inequalities

Absolute Value Equations and Inequalities

• Solving an absolute value equation
• Solving an absolute value “less than” inequality
• Solving an absolute value “greater than” inequality

The Rectangular Coordinate System

• Plotting ordered pairs
• Finding intercepts of a graph given an equation
• Finding the midpoint of a line segment using the midpoint formula
• Finding the distance between two points using the distance formula

Circles

• Writing the standard form of an equation of a circle
• Sketching the graph of a circle
• Converting the general form of a circle into standard form

Lines

• Determining the slope of a line
• Sketching a line given a point and the slope
• Finding the equation of a line using the point-slope form
• Finding the equation of a line using the slope-intercept form
• Writing the equation of a line in standard form
• Finding the slope and the y-intercept of a line in standard form
• Sketching lines by plotting intercepts
• Finding the equation of a horizontal line and a vertical line

Parallel and Perpendicular Lines

• Understanding the definition of parallel lines
• Understanding the definition of perpendicular lines
• Determining whether two lines are parallel, perpendicular, or neither
• Finding the equations of parallel and perpendicular lines

Relations and Functions

• Understanding the definitions of relations and functions
• Determining whether equations represent functions
• Using function notation; evaluating functions
• Using the vertical line test
• Determining the domain of a function given the equation

Properties of a Function’s Graph

• Determining the intercepts of a function
• Determining the domain and range of a function from its graph
• Determining whether a function is increasing, decreasing, or constant
• Determining relative maximum and relative minimum values of a function
• Determining whether a function is even, odd, or neither
• Determining information about a function from a graph

Graphs of Basic Functions; Piecewise Functions

• Sketching the graphs of the basic functions
• Sketching the graphs of basic functions with restricted domains
• Analyzing piecewise-defined functions

Transformations of Functions

• Using vertical shifts to graph functions
• Using horizontal shifts to graph functions
• Using reflections to graph functions
• Using vertical stretches and compressions to graph functions
• Using combinations of transformations to graph functions

Composite Functions

• Forming and evaluating composite functions
• Determining the domain of composite functions

One-to-One Functions; Inverse Functions

• Understanding the definition of a one-to-one function
• Determining whether a function is one-to-one using the horizontal line test
• Understanding and verifying inverse functions
• Sketching the graphs of inverse functions
• Finding the inverse of a one-to-one function

• Understanding the definition of a quadratic function and its graph
• Graphing quadratic functions written in vertex form
• Graphing quadratic functions using the vertex formula
• Determining the equation of a quadratic function given its graph

Applications and Modeling of Quadratic Functions

• Maximizing projectile motion functions
• Maximizing functions in economics

The Graphs of Polynomial Functions

• Understanding the definition of a polynomial function
• Sketching the graphs of power functions
• Determining the end behavior of polynomial functions
• Determining the intercepts of a polynomial function
• Determining the real zeros of polynomial functions and their multiplicities
• Sketching the graph of a polynomial function
• Determining a possible equation of a polynomial function given its graph

Rational Functions and Their Graphs

• Finding the domain and intercepts of rational functions
• Identifying vertical asymptotes
• Identifying horizontal asymptotes
• Using transformations to sketch the graphs of rational functions
• Finding removable discontinuities, intercepts, asymptotes and sketch graphs of rational functions

Exponential Functions

• Understanding the characteristics of exponential functions
• Sketching the graphs of exponential functions using transformations
• Solving exponential equations by relating the bases
• Solving applications of exponential functions

Logarithmic Functions

• Understanding the definition of a logarithmic function
• Evaluating logarithmic expressions
• Understanding the properties of logarithms
• Using the common and natural logarithms
• Understanding the characteristics of logarithmic functions
• Sketching the graphs of logarithmic functions using transformations
• Finding the domain of logarithmic functions

Properties of Logarithms

• Using the product rule, quotient rule, and power rule for logarithms
• Expanding and condensing logarithmic expressions
• Solving logarithmic equations using the logarithm property of equality
• Using the change of base formula

Exponential and Logarithmic Equations

• Solving exponential equations
• Solving logarithmic equations

Applications of Exponential and Logarithmic Functions

• Solving compound interest applications
• Solving exponential growth and decay applications

Systems of Equations

• Verifying solutions to a system of linear equations in two variables
• Solving a system of linear equations using the substitution method
• Solving a system of linear equations using the elimination method
• Solving applied problems using a system of linear equations