2. Equations and Inequalities

Understanding the Viewing Rectangle

Graphs and Graphing Utilities

X-Intercepts and Y-Intercepts of a Functions and Finding Them! Example 2

Graphing Linear Functions by Finding X,Y Intercept

How to Plot a Point in the X-Y Plane

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x^3 - 1

Graphs and Graphing Utilities - Interpret Information Given by Graphs

In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 4, 0)

Graphing Equations by Plotting Points - Example 1

The Cartesian Coordinate System - The Basics!

In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 5/2, 3/2)

Graphing Equations by Plotting Points - Example 3

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x^2 + 2

Make Sense? In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.

I used the ordered pairs (- 2, 2), (0, 0), and (2, 2) to graph a straight line.

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = -2|x|

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/a59e5da6c9b8ff08-1672680578903.jpg" alt="" />

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = 9 - x^2

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/cb39650e31aaa47c-1672681225542.jpg" alt="" />

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation.

The y-value is two more than the square of the x-value.

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation.

The y-value is three decreased by the square of the x-value.

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/a942bd2a1cf29646-1672680848299.jpg" alt="" />

Interpreting Graphs of Functions

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation.

y = 5 (Let x = -3, - 2, - 1, 0, 1, 2, and 3.)

Basic Math - Graphing with a Ti-83 or Ti-84 Calculator

Graph a Line by Plotting Points - Example 2

Selecting a Viewing Window

Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = 2x-2

Finding Intercepts from the Graph of Functions

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x + 2

In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

The ordered pair (2, 5) satisfies 3y - 2x = - 4.

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = |x| + 1

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 

y = - (1/2)x + 2

Finding x and y Intercepts from a Graph 1.5

In Exercises 1-12, plot the given point in a rectangular coordinate system. (0, -3)

In Exercises 1-12, plot the given point in a rectangular coordinate system. (7/2, - 3/2)

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = -(1/2)x

Graphing Using the Point Plot Method

Graph Points in Any Quadrant

Graphing in Algebra: Ordered Pairs and the Coordinate Plane

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/15cc67b8bdf27bf9-1672247682203.jpg" alt="" />

In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 2, 3)

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/eb6d8f1ba13c7d53-1672681605065.jpg" alt="" />

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x^3

Graph Points on a Coordinate Plane

In Exercises 1-12, plot the given point in a rectangular coordinate system. (1, 4)

Intercepts of Graphs and Where the Function is Positive and/or Negative

Identify the X and Y Intercepts on a Graph

Graphing a Linear Equation using Intercepts

In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each graph, tick marks along the axes represent one unit each.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/3f965bd4d94ee7dc-1671715630122.jpg" alt="" />

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation.

The y-value is the difference between four and twice the x-value.

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation.

The y-value is four more than twice the x-value.

In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 4, - 2)

Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = x^2-3

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/bd0ff59539b67f68-1672247261808.jpg" alt="" />

Understand line graphs by interpreting their scales

In Exercises 75–78, list the quadrant or quadrants satisfying each condition.

x^3 > 0 and y^3 <0

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x - 2

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x^2 - 2

X-Intercepts and Y-Intercepts of a Functions and Finding Them! Example 1

Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = |x|-2

In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each graph, tick marks along the axes represent one unit each.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/aaab59be183f87e1-1670957749202.jpg" alt="" />

Interpreting Line Graphs

Write Coordinate Pairs for Points

Graph quadratic functions using a graphing calculator

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

College Algebra

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1. Fundamental Concepts of Algebra

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

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Solve Quadratic Equations by Factoring

Solve Quadratic Equations by the Square Root Property

Solve Quadratic Equations by Completing the Square

Solve Quadratic Equations Using the Quadratic Formula

Use the Discriminant to Determine the Number and Type of Solutions

Determine the Most Efficient Method to Use When Solving a Quadratic Equation

Solve Problems Modeled by Quadratic Equations

Quadratic Equations

Add and Subtract Complex Numbers

Multiply Complex Numbers

Divide Complex Numbers

Simplify square roots of negative numbers.

Perform Operations with Square Roots of Negative Numbers

Simplify powers of i

Complex Numbers

Solving Linear Equations in One Variable

Solving a Linear Equation Involving Fractions

Solve Rational Equations with Variables in the Denominators

Recognize Identities, Conditional Equations, Inconsistent Equations

Solve Applied Problems Using Mathematical Models

Linear Equations and Rational Equations

Use Interval Notation

Find Intersections and Unions of Intervals

Solve Linear Inequalities

Rationalize Inequalities with No Solution 

Solve Compound Inequalities

Solve Absolute Value Inequalities

Linear Inequalities and Absolute Value Inequalities

Plotting Points in the Rectangular Coordinate System

Graphing an Equation Using the Point-Plotting Method

Identifying Intercepts

Interpret Information Given by Graphs

Solving Polynomial Equations by Factoring

Solve Radical Equations

Solve Equations with Rational Exponents

Solve Equations That Are Quadratic In Form

Solving Equations Involving Absolute Value

Solve Problems Modeled by Equations

Other Types of Equations

Use Linear Equations to Solve Problems

Solve a Formula for a Variable

Models and Applications

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