3. Functions and Graphs

Understand and Use Piecewise Functions

Basics of Functions and Their Graphs

Evaluating Piecewise Defined Functions

Symmetry - A Quick Discussion for Testing if a Polynomial is Even / Odd

In Exercises 95–96, let f and g be defined by the following table: Find √(ƒ(−1) − f(0)) – [g (2)]² + ƒ(−2) ÷ g (2) · g (−1) .

Domain and Range in Set Notation Tutorial

Identify functions using algebra

In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16

Identify functions in various forms

Describe the rate of change of linear and non-linear functions

Increasing/Decreasing , Local Maximums/Minimums

Definition of a Function

Ex 2:  Determine a Function Value From a Graph

Determine whether each relation is a funciton, Give the domain and range for each relation. (1, 10), (2, 500), (13, π)

❖ The Difference Quotient - Example 1 ❖

Domain and Range - Basic Idea - Two Graph Examples

Finding intercepts of a nonlinear function given its graph

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation.{(1, 2), (3, 4), (5, 5)} 

Identify polynomial extrema

Find the Formula for a Piecewise Function from Graph

Determine whether each equation defines y as a function of x. 2x + y^2 = 6

Local and Absolute Maximum and Minimum from a Graph

The Vertical Line Test

Finding the Domain and Range of a Piecewise Function

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(-3, -3), (-2, −2), (−1, −1), (0, 0)}

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3

c. f(x-6)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3

b. f(10)

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(1, 4), (1, 5), (1, 6)}

Graph piecewise functions

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3|

a. f(5)

 Determining If a Relation is Also a Function - Verbal Descriptions

Even Odd or Neither from graph

Graphing Functions by Plotting Points - Linear 

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3|

b. f(-5)

The Difference Quotient - Example 2

Determining If a Relation is Also a Function - Equation Format

Recognize functions

Find domain and range of a function using a graph

Identify a relation as a function

Graphing a Piece-Wise Defined Function - Another Example

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(3, −2), (5, −2), (7, 1), (4, 9)}

Testing an Equation for Symmetry

Describe function relationships using graphs

Determine whether each equation defines y as a function of x. 2x + y = 8

Graphing Equations by Plotting Points - Example 1

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x^4 - x²+1

c. h (-x)

Domain and range from the graph of a discrete relation

Adding and Subtracting Functions - Function Notation

Evaluate a function given an input value

Finding Domain and Range of a Function using a Graph

Graphing Equations by Plotting Points - Example 3

Identify functions given sets, mappings, and real world scenarios

Graph a Line by Plotting Points - Example 2

Graph piecewise-defined functions

In Exercises 11–26, determine whether each equation defines y as a function of x. y = - √x +4

Find intervals that a function is increasing and decreasing

ACT PREP - Find the Domain of a Function

 Using a Graph to Determine Values of a Function

How to calculate the difference quotient

In Exercises 95–96, let f and g be defined by the following table: Find |ƒ(1) − f(0)| − [g (1)]² +g(1) ÷ ƒ(−1) · g (2) .

Recognize functions using the vertical line test

What Is Function Notation?

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 

d. h (3a)

Finding Intercepts from the Graph of Functions

In Exercises 11–26, determine whether each equation defines y as a function of x. x+y³ = 8

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(3, 4), (3, 5), (4, 4), (4, 5)} 

The Difference Quotient - Example 1

Evaluate each function at the given values of the independent variable and simplify. g(x) = 3x^2 - 5x + 2 (a) g(0), (b) g(-2), (c) g(x-1), (d) g(-x)

In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g(-1) and f(g(-1)).

Graphing functions by plotting points

Even/Odd Functions

Determining If a Relation is Also a Function - Ordered Pairs1

Distinguish between even and odd functions

Determining If a Relation is Also a Function

How to determine the intervals that a function is increasing decreasing or constant

In Exercises 11–26, determine whether each equation defines y as a function of x. y = √x +4

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3|

c. f(−9 - x)

Determine the domain and range of a parabola: looking at the graph

Testing an equation for symmetry about the axes and origin

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 

c. h (-x)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x^4 - x²+1

d. h (3a)

Simplify: 2(x+h)² + 3 (x + h) + 5 − (2x² + 3x + 5).

Determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of those, or none of these. x^2 + y^2 =17

In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).

Graphing in Algebra: Ordered Pairs and the Coordinate Plane

GC3 - Investigating a Function

Determine domain and range and if a relation is a function

Using Function Notation

Find Intercepts, Domain and Range, Intervals Increasing, Decreasing or Constant

Relations, Domain and Range - Grade 11 Functions

Evaluate functions written in function notation

How to Compute the Difference Quotient (f(x + h) - f(x))/h

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

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

Find Slopes and Equations of Parallel and Perpendicular Lines

Interpret Slope as Rate of Change

Find a Function's Average Rate of Change

More on Slope

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

Find and Simplify a Function's Different Quotient

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

General Chemistry

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Study the key concepts of Physics with descriptive videos, questions, and more

Physics

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General Biology

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Financial Accounting

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Dive deep into Psychology with videos, practice problems, and more.

Psychology

Microeconomics

The first in a two-course sequence introduces the basic structure and functions of the human body

Anatomy & Physiology

College Algebra covers algebraic topics and skills necessary to succeed in college-level math