3. Functions and Graphs

Find Slopes and Equations of Parallel and Perpendicular Lines

More on Slope

 Relationship Between Slopes of Non-Vertical Parallel Lines

Determining the constant rate of change

Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 9.

Describe the rate of change of a linear function

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

average rate of change

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. vertical, through (-6, 4)

Graphing Parallel and Perpendicular Lines

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. y = (2/5)x - 1

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-5,4), m = -3/2

Relationship Between Slopes of Non-Vertical Perpendicular Lines

Write the equations of parallel lines

IB Sample Exam Question, Paper 1 Q5

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. x-intercept (3,0), y-intercept (0,-2)

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-2,5) having slope -4

Determine rate of change in linear relationships

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. horizontal, through (-7,4)

Find average rates of change using data in tables

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. m=5, b=15

Calculate average rate of change using d=rt

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-8,4), undefined slope

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (5,-8), m = 0

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. 2x + 3y + 6 = 0

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. slope 0, y-intercept (0, 3/2)

Write the equations of perpendicular lines

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

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1. Fundamental Concepts of Algebra

2. Equations and Inequalities

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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Verify Inverse Functions

Find the Inverse of a Function

Determine if a Function Has an Inverse Function (Using Horizontal Line)

Graph Inverse Function (use one-to-One Function graph)

Find the Inverse of a Function and Graph Both Functions 

Inverse Functions

Interpret Slope as Rate of Change

Find a Function's Average Rate of Change

Recognizing Graphs of Common Functions

Use Vertical Shifts to Graph Functions

Use Horizontal Shifts to Graph Functions

Use Reflections to Graph Functions

Use Vertical Stretching and Shrinking to Graph Functions

Use Horizontal Stretching and Shrinking to Graph Functions

Graph Functions Involving a Sequence of Transformations

Transformations of Functions

Find the Domain of a Function

Combine Functions Using the Algebra of Function

Form Composite Functions

Determine Domains for Composite Functions

Write Functions as Compositions

Combinations of Functions; Composite Functions

Find the Domain and Range of a Relation

Determine Whether a Relation is a Function

Determine Whether an Equation Represents a Function

Evaluate a Function

Graph Functions by Plotting Points

Use the Vertical Line Test to Identify Functions

Obtain Information About a Function From Its Graph

Identifying the Domain and Range of a Function From Its Graph

Identify Intercepts from a Function's Graph

Identify Intervals on Which a Function Increases, Decreases, or Is Constant

Use Graphs to Locate Relative Maxima or Minima

Test for Symmetry

Identifying Even or Odd Functions and Recognize Their Symmetries

Understand and Use Piecewise Functions

Find and Simplify a Function's Different Quotient

Basics of Functions and Their Graphs

Calculate a Line's Slope

Write the Point-Slope Form of the Equation of a Line

Write and Graph the Slope-Intercept Form of the Equation of a Line

Graph Horizontal and Vertical Lines

Recognize and Use the General Form of a Line's Equation

Use Intercepts to Graph the General Form of a Line's Equation

Model Data with Linear Functions and Make Predictions

Linear Functions and Slope

Find the Distance Between Two Points

Find the Midpoint of a Line Segment

 Standard Form of a Circle's Equation

Center and Radius of a Circle Whose Equation Is in Standard Form

Convert the General Form of a Circle's Equation to Standard Form

Distance and Midpoint Formulas; Circles

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