ORCCAOpen Resources for Community College Algebra

Relations and Functions

1. Use the definition of a function to determine whether a given relation represents a function

2. Determine the domain and range of functions given as a graph, given as a set of ordered pairs, and given as a table

3. Apply function notation in graphical, algebraic, and tabular settings

   1. Understand the difference between the input and output

   2. Identify ordered pairs from function notation

   3. Given an input, find an output

   4. Given an output, find input(s)

4. Interpret function notation in real world applications

   1. Evaluate the function at a particular input value and interpret its meaning

   2. Given a functional value (output), find and interpret the input

Linear Equations and Functions

1. Solve linear equations and inequalities in one variable

2. Graph linear functions

   1. Graph a linear function by finding the intercepts

   2. Graph a linear function given its slope and the vertical intercept

   3. Create graphs where the axes are required to have different scales (e.g. Slope of \(10\) with scale of \(1\) on the \(x\)-axis and different scale on the \(y\)-axis.)

   4. Graph a linear function given its slope and a point on the line

3. Determine the slopes of lines from equations and graphs and interpret their significance as rates of change

4. Determine linear functions

   1. Find an equation for a linear function given a graph of the function

   2. Find an equation for a linear function given two points

   3. Find an equation for a linear function given a verbal description of a linear relationship, first identifying the independent and dependent variables

5. Solve systems of linear equations in two variables

   1. Solve systems by graphing

   2. Solve systems by the substitution method

   3. Solve systems by the addition (elimination) method

6. Applications of linear equations of one variable, linear functions, and systems of linear equations

Quadratic Equations and Functions

1. Review polynomial operations, laws of exponents, and factoring polynomial expressions

   1. Factor expressions having a greatest common factor

   2. Factor binomials

      1. Differences of squares

      2. Sums and differences of cubes

   3. Factor trinomials with leading coefficients of \(1\) as well as leading coefficients not \(1\)

   4. Factor multivariable expressions

2. Solve quadratic equations in one-variable

   1. Solve quadratic equations using the square root property

   2. Solve quadratic equations by factoring

   3. Solve quadratic equations using the Quadratic Formula including complex solutions

      1. Simplify and approximate non-variable square roots including complex solutions

      2. Use the Pythagorean Theorem to find missing sides of a right triangle, then use the lengths to write the sine, cosine, and tangent of an angle within the triangle

3. Graph quadratic functions

   1. Graph a quadratic function from an equation by creating a table and plotting points

   2. Graph a quadratic function by finding the axis of symmetry, the vertex and the intercepts

   3. Use and interpret quadratic models of real world situations algebraically and graphically

      1. Evaluate the function at a particular input value and interpret its meaning

      2. Given a functional value (output), find and interpret the input

      3. Interpret the vertex, the vertical intercept, and any horizontal intercept(s) using proper units

Literal Equations and Formulas

1. Solve an equation for a specified variable in terms of other variables

2. Input values into a formula and solve for the remaining variable