Question

The function f(x) = 6x + 8 is transformed to function g through a horizontal stretch by a factor of 5. What is the equation of function g? Replace the values of a and k in the function equation

Answer 1

f(1/5x) = 6 ^1/5x +8

Explanation:

A horizontal stretch by a factor of 5 means that the input, or x, is multiplied by : 1/5

Answer 2

`g(x) = (6)/(5)x + 8`

Explanation:

Given

`f(x) = 6x + 8`

`k = 5` --- horizontal stretch factor

Required

Find g(x)

When a function is stretched horizontally by k, the resulting function will be:

Rule:
`g(x) = f((1)/(k)x)`

So, we have:

`g(x) = f((1)/(5)x)`

Solve for:
`f((1)/(5)x)`

`f((1)/(5)x) = 6 * (1)/(5)x + 8`

`f((1)/(5)x) = (6)/(5)x + 8`

Recall that:

`g(x) = f((1)/(5)x)`

`g(x) = (6)/(5)x + 8`