Question

F(x) = 7x g(x) = 7x + 6 Which statement about f(x) and its translation, g(x), is true?

Answer 1

f(x) is shifted left by
`(6)/(7)` units on x-axis.

Explanation:

The functions f(x) = 7x g(x) = 7x + 6 have been given in the question.

g(x) is translation of f(x) we have find the translation done.

(1) Since both are linear functions having same slope so lines represented byu functions are parallel.

(2) f(x) passes through origin ( 0,0 )

(3) g(x) touches x-axis at y = 0

or 0 =7x + 6 ⇒ x = -6/7

therefore, f(x) = 7x is the parent function which passes through origin has been shifted left by (
`(6)/(7)`) units on x-axis.

Answer 2

The graph of the function g(x) is the same as the graph of the function f(x) after a translation up of 7 units.
The general rule is the following:
Suppose given a function f(x) and another function g(x) defined as:
g(x)=f(x)+a, wherein a is a constant. Then the graph of g is the translation up of "a" unit of the graph of f.