Question

PLEASE HELP!! Write an equation of g(x) that represents an exponential base “e” parent function with the following transformations:
Reflect over y-axis, shift right 7, vertical stretch by 12

Answer 1

Answer:

$g(x) = 12 {e}^{ - x - 7}$

Step-by-step explanation:

The parent function is

$g(x) = e {}^{x}$

First it is asked to reflect over the y axis so using the rule

$g(x) = g( - x)$

Our function looks like

$g(x) = e {}^{ - x}$

Then we are asked to shift the equation to the right 7. When shifting to the right or move the x axis, instead of adding 7 we would want to subtract 7 since the x axis is the independent variable and we must respect the y axis which is the dependent so using the rule

$g(x) = g(x - h)$

When subtracting a 7 it looks like now

where h is the number we move . Now we are asked to apply a vertical stretch of 12. Since vertical stretch refers to the y axis, we are just going to multiply the function by 12 using the rule

$g(x) = a \times g(x)$

where a is the vertical stretch. So now it would look like

$g(x) = 12 {e}^{ - x - 7}$