Transformations of linear functions worksheet with answers

Problem 1 : 

Graph f(x) = x and g(x) = x - 5. Then describe the transformation from the graph of f(x) to the graph of g(x).

Problem 2 : 

Graph f(x) = x + 2 and g(x) = 2x + 2. Then describe the transformation from the graph of f(x) to the graph of g (x) .

Problems 3-4 : Graph f(x). Then reflect the graph of f(x) across the y-axis. Write a function g(x) to describe the new graph.

Problem 3 : 

f(x)  =  x

Problem 4 : 

f(x)  =  -4x - 1

Problem 5 : 

Graph f(x) = x and g(x) = 3x + 1. Then describe the transformations from the graph of f(x) to the graph of g(x).

Problem 6 : 

A trophy company charges $175 for a trophy plus $0.20 per letter for the engraving. The total charge for a trophy with x letters is given by the function f(x) = 0.20x + 175. How will the graph change if the trophy’s cost is lowered to $172? if the charge per letter is raised to $0.50?

Detailed Answer Key

1. Answer : 

The graph of g(x) = x - 5 is the result of translating the graph of f(x) = x, 5 units down.

2. Answer : 

The graph of g(x) = 2x + 2 is the result of rotating the graph of f(x) = x + 2 about (0, 2). The graph of g(x) is steeper than the graph of f(x).

3. Answer : 

To find g(x), multiply the value of m by -1.

In f(x) = x, m = 1.

1(-1)  =  -1   This is the value of m for g(x).

g(x) = -x

4. Answer : 

To find g(x), multiply the value of m by -1.

In f(x) = -4x - 1, m = -4.

-4(-1)  =  4   This is the value of m for g(x).

g(x) = 4x - 1 

5. Answer : 

Find transformations of f(x) = x that will result in g(x) = 3x + 1 :

• Multiply f(x) by 3 to get h(x) = 3x. This rotates the graph about (0, 0) and makes it steeper.

• Then add 1 to h(x) to get g(x) = 3x + 1. This translates the graph 1 unit up.

The transformations are a rotation and a translation.

6. Answer : 

f(x) = 0.20x + 175 is graphed in blue.

If the trophy’s cost is lowered to $172, the new function is g(x) = 0.20x + 172. The original graph will be translated 3 units down. 

If the charge per letter is raised to $0.50, the new function is h(x) = 0.50x + 175. The original graph will be rotated about (0, 175) and become steeper.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to 

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

All Algebra II Resources

Shift the equation  up three units and left six units.  What is the new equation?

Correct answer:

Explanation:

Rewrite the equation in slope intercept form.

Shifting the graph up by three units will require adding three to the y-intercept.

Shifting the graph left six units mean that the x-variable will need to be replaced with:  

The equation becomes:

Simplify this equation.

The answer is:  

Shift the graph  down six units.  What is the new equation?

Correct answer:

Explanation:

Rewrite the given equation in standard form to slope-intercept form.

Subtract  from both sides.

Divide by three on both sides.

Simplify this equation.

Shifting this equation down means that the y-intercept will be subtracted six.

The answer is:  

Translate the graph  down fifteen units.  What is the new equation?

Correct answer:

Explanation:

The given equation can be rewritten in slope-intercept format, .

Shifting down a line fifteen units will decrease the y-intercept by 15.

The answer is:  

Translate the graph  left four units and up one unit.  What's the new equation?

Correct answer:

Explanation:

Shifting the equation up one unit will change the y-intercept by adding one.

If the graph is to be shifted four units to the left, the x-variable will need to be replaced with the quantity .

Use the distribution property to simplify the binomial.

The equation is:  

Shift the function  up four units.  What is the new equation?

Correct answer:

Explanation:

Rewrite this equation in standard form to slope intercept format.

Subtract  on both sides.

Divide by three on both sides.

Simplify this equation.

If this graph is shifted up four units, simply add four to the y-intercept.

The answer is: 

Shift  left eight units.  What is the new equation?

Correct answer:

Explanation:

Shifting the graph left 8 units will require changing the x-variable to .

Replace the term and simplify the equation.

Distribute the six through the binomial.

The equation is:  

Translate the function  left 5 units.  What is the new equation?

Correct answer:

Explanation:

If the graph is shifted leftward, apply the transformation by replacing the x-variable with .

Simplify this equation by distribution, and rewrite this in slope intercept format.

Combine like-terms.

The answer is:  

Translate the line  down three units and left four units.  What is the new equation?

Correct answer:

Explanation:

Rewrite the equation in slope-intercept form:  

Shifting this line down three units will decrease the y-intercept by three.

If the line is shifted left four units, the x-variable will need to be replaced with .

Simplify this equation.

The answer is:  

Translate the line  left three units and down four units.  What is the new equation?

Correct answer:

Explanation:

Rewrite the given equation in standard form to slope-intercept form.

Add  on both sides.

A shift down four units will decrease the y-intercept by four.  The current y-intercept is zero.  Rewrite the equation.

The line shifted three units to the left means that the x-variable will need to be replaced with .

Rewrite the equation.

Simplify this equation.

The answer is:  

Translate the graph  up three units.  What is the new equation?

Correct answer:

Explanation:

Simplify the equation by distribution.

Shifting this line up by three units will add three to the y-intercept.

The answer is:  

All Algebra II Resources