Question

Match each verbal description to its equivalent function rule as applied to the given function below.

f(x)=7x+5

a. g(x)=7x-18
b. g(x)=21x+17
c. g(x)=14x+7
d. g(x)=7x+14
e. g(x)=-7x-16
f. g(x)=-7x+16


a. The function f stretched vertically by a factor of 3 and translated up by 2 units.
b. The function f translated 2 units down and 3 units right.
c. The function f stretched vertically by a factor of 2 and translated down by 3 units.
d. The function f reflected about the y-axis ← and translated 3 units left.

Answer 1

To match each verbal description to its equivalent function rule, we analyze the given options and determine which ones correspond to the desired transformations of the function f(x)=7x+5.

Step-by-step explanation:

To match each verbal description to its equivalent function rule, we need to identify the transformations applied to the function f(x)=7x+5. Let's analyze each option:

a. The function f stretched vertically by a factor of 3 and translated up by 2 units: This corresponds to g(x)=21x+17.

b. The function f translated 2 units down and 3 units right: This corresponds to g(x)=7x-18.

c. The function f stretched vertically by a factor of 2 and translated down by 3 units: This corresponds to g(x)=14x+7.

d. The function f reflected about the y-axis and translated 3 units left: This corresponds to g(x)=7x+14.

e. The function g(x)=-7x-16 is not a valid transformation of f(x).

f. The function g(x)=-7x+16 is not a valid transformation of f(x).