# Math 1021 College Algebra Topics

**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

**Quadratic Equations **

- Solving quadratic equations by factoring and the zero product property
- Solving quadratic equations using the square root property
- Solving quadratic equations using the quadratic formula
- 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

**Quadratic Functions **

- 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