Given f(x)=6x+5, describe how the graph of g compares with the graph of f.
g(x)=6(0.2x)+5
Select the correct choice below, and fill in the answer box to complete your choice.
A. The graph of g(x) is translated _ unit(s) to the left compared to the graph of f(x).
B. The graph of g(x) is translated _ unit(s) down compared to graph of f(x).
C. g(x) has a scale factor of _ compared to f(x). Because it scales the vertical direction, the graph is stretched vertically.
D. g(x) has a scale factor of _ compared to f(x). Because it scales the vertical direction, the graph is compressed vertically.
E. g(x) has a scale factor of _ compared to f(x). Because it scales the horizontal direction, the graph is stretched horizontally.
F. g(x) has a scale factor of _ compared to f(x). Because it scales the horizontal direction, the graph is compressed horizontally.
G. The graph of g(x) is translated _ unit(s) to the right compared to the graph of f(x).
H. The graph of g(x) is translated _ unit(s) up compared to graph of f(x).
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