Question

The function f(x)=2x−5 is a linear function. Let g(x) represent f(x) after a horizontal translation 3 units to the right.

What is the equation for g(x)?



Enter the answer in the box.

g(x)=____

Answer 1

gx= 2x-2

Shall be the new parallel equation

Answer 2

The equation for g(x) after a horizontal translation 3 units to the right of f(x) is 2x-11.

Explanation:

If y = f(x), then y = f(x-h) gives a horizontal translation which results in a graph that is equivalent to shifting the base graph left or right in the direction of the x-axis.

Given linear function f(x) = 2x−5

g(x) represent f(x) after a horizontal translation 3 units to the right that is

g(x) = 2(x-3)-5

g(x) = 2x-6-5

g(x)= 2x-11

The graph plot below shows the horizontal translation of the function f(x) 3 units to the right.

Thus, the equation for g(x) after a horizontal translation 3 units to the right of f(x) is 2x-11.