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

Answer:

$g(x) = \frac{6}{5}x + 8$

Step-by-step 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: $g(x) = f(\frac{1}{k}x)$

So, we have:

$g(x) = f(\frac{1}{5}x)$

Solve for: $f(\frac{1}{5}x)$

$f(\frac{1}{5}x) = 6 * \frac{1}{5}x + 8$

$f(\frac{1}{5}x) = \frac{6}{5}x + 8$

Recall that:

$g(x) = f(\frac{1}{5}x)$

$g(x) = \frac{6}{5}x + 8$

Answer 2

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