Answer:
[tex]g(x) = \frac{6}{5}x + 8[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6x + 8[/tex]
[tex]k = 5[/tex] --- horizontal stretch factor
Required
Find g(x)
When a function is stretched horizontally by k, the resulting function will be:
Rule: [tex]g(x) = f(\frac{1}{k}x)[/tex]
So, we have:
[tex]g(x) = f(\frac{1}{5}x)[/tex]
Solve for: [tex]f(\frac{1}{5}x)[/tex]
[tex]f(\frac{1}{5}x) = 6 * \frac{1}{5}x + 8[/tex]
[tex]f(\frac{1}{5}x) = \frac{6}{5}x + 8[/tex]
Recall that:
[tex]g(x) = f(\frac{1}{5}x)[/tex]
[tex]g(x) = \frac{6}{5}x + 8[/tex]
Answer:
f(1/5x) = 6 ^1/5x +8
Step-by-step explanation:
A horizontal stretch by a factor of 5 means that the input, or x, is multiplied by : 1/5
