Answer:
[tex]g(x) = 12 {e}^{ - x - 7} [/tex]
Step-by-step explanation:
The parent function is
[tex]g(x) = e {}^{x} [/tex]
First it is asked to reflect over the y axis so using the rule
[tex]g(x) = g( - x)[/tex]
Our function looks like
[tex]g(x) = e {}^{ - x} [/tex]
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
[tex]g(x) = g(x - h)[/tex]
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
[tex]g(x) = a \times g(x)[/tex]
where a is the vertical stretch. So now it would look like
[tex]g(x) = 12 {e}^{ - x - 7} [/tex]
