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0. Review of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

1. Equations & Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs of Equations(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

Dividing Polynomials
(0)

Zeros of Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential & Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Systems of Equations & Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

8. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

9. Sequences, Series, & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

10. Combinatorics & Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

3. Functions

Intro to Functions & Their Graphs

3. Functions

Intro to Functions & Their Graphs: Videos & Practice Problems

Video Lessons Practice Worksheet

277 problems

Problem types you want to practice:

Problem 181Multiple Choice

Graph the following function:

Piecewise function definition with three segments for f(x).

Problem 182Multiple Choice

Graph the following function:

Piecewise function f(x) with two conditions displayed in a mathematical format.

Problem 183Multiple Choice

For the following graph, write its equivalent piecewise function and write its domain and range.

Graph showing a piecewise function with horizontal lines at y=-3 and y=5.

Problem 184Multiple Choice

For the following graph, write its equivalent piecewise function and write its domain and range.

Graph showing a piecewise function with points at (-3,12), (-2,8), and (0,-5).

Problem 185Multiple Choice

Evaluate the value of the following function for x = 6.4

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mn>8</mn><mo> </mo><mi>if</mi><mo> </mo><mn>0</mn><mo><</mo><mi>x</mi><mo>≤</mo><mn>4</mn><mo>,</mo></mtd></mtr><mtr><mtd><mn>15</mn><mo>-</mo><mn>3</mn><mfenced open=\"[\" close=\"]\"><mfenced open=\"[\" close=\"]\"><mrow><mn>4</mn><mo>-</mo><mn>8</mn><mi>x</mi></mrow></mfenced></mfenced><mo> </mo><mi>if</mi><mo> </mo><mi>x</mi><mo>></mo><mn>4</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

where [[.]] is the greatest integer function.

Problem 186Multiple Choice

Evaluate the value of the following function for x = 9.4

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mn>7</mn><mo> </mo><mi>if</mi><mo> </mo><mn>0</mn><mo><</mo><mi>x</mi><mo>≤</mo><mn>6</mn><mo>,</mo></mtd></mtr><mtr><mtd><mn>12</mn><mo>-</mo><mn>2</mn><mfenced open=\"[\" close=\"]\"><mfenced open=\"[\" close=\"]\"><mrow><mn>8</mn><mo>-</mo><mi mathvariant=\"normal\">x</mi></mrow></mfenced></mfenced><mo> </mo><mi>if</mi><mo> </mo><mi>x</mi><mo>></mo><mn>6</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

where [[.]] is the greatest integer function.

Problem 187Multiple Choice

Graph the greatest integer function given below. Write the domain and range of the function.

f(x ) = -[[5x]]

Problem 188Multiple Choice

Graph the greatest integer function given below. Write the domain and range of the function.

f(x ) = [[4x - 1]]

Problem 189Multiple Choice

The cost of x ounces (x > 0) of tea is expressed as f(x) = 45 - 12[[3 - x]] cents. Find the cost of 3.5-ounces of tea.

Problem 190Multiple Choice

Identify if the given graph represents a function. Also, find the domain and range.

Graph showing a circle centered at (20, 10) with radius 10, questioning if it's a function.

Problem 191Multiple Choice

Identify if the given graph represents a function. Also, find the domain and range.

Graph showing two parabolas; question on function identification and domain/range.

Problem 192Multiple Choice

Identify if the given graph represents a function. Also, find the domain and range.

Graph showing a function with domain and range annotations for college algebra.

Problem 193Multiple Choice

Identify if the given graph represents a function. Also, find the domain and range.

Graph showing a function with points (0,2) and (0,4) on the axes.

Problem 194Multiple Choice

Graph the following equation. 6x + 12y = 48

Problem 195Multiple Choice

Graph the following equation. 5y = 2x

Problem 196Multiple Choice

Graph the following equation. f(x) = 10x

Problem 197Multiple Choice

Graph the following equation. 2x - 5y = 30

Problem 198Multiple Choice

Graph the following equation. x = - 17

Problem 199Multiple Choice

Graph the following equation. f(x) = - 17

Problem 200Multiple Choice

Graph the following equation. f(x) = |2x| + 5

Problem 201Multiple Choice

Graph the following equation. f(x) = 5∛(x - 8) + 5

Problem 202Multiple Choice

Graph the following equation.

Piecewise function definition with absolute value and linear equations.

Problem 203Multiple Choice

Identify if the graph defined by the following equation is symmetric with respect to the origin, x-axis, y-axis, or none:

3y⁵ = x - 7

Problem 204Multiple Choice

Identify if the graph defined by the following equation is symmetric with respect to the origin, x-axis, y-axis, or none:

|3x| = |17y|

Problem 205Multiple Choice

Draw the graph for the given functions f and g in the same rectangular system and state the relation between both graphs.

f(x) = (√3)(x), g(x) = (√3)(x) +5

Problem 206Multiple Choice

Draw the graphs for the given functions f and g in the same rectangular system and state the relation between both graphs.

f(x) = -5x, g(x) = -5x -6

Problem 207Multiple Choice

Find the value of f(3) using the graph shown below.

Graph of a function showing f(3) to find its value in college algebra.

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Problem 208Multiple Choice

Find the x-intercept and the y-intercept of the function using the graph given below.

Graph showing x-intercept at (10,0) and y-intercept at (0,-10) for function analysis.

Problem 209Multiple Choice

Find the x-intercept and the y-intercept of the function using the graph given below.

Graph showing x-intercept at (5,0) and y-intercept at (0,7) for function analysis.

Problem 210Multiple Choice

Find the domain and the range of the function using the graph given below.

Graph of a function showing its domain and range for college algebra topic on functions.

Lines Practice Problems Common Functions Practice Problems

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Intro to Functions & Their Graphs: Videos & Practice Problems

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