Question

Question 9 of 10If you apply these changes to the linear parent function, f(x) = x, what is theequation of the new function?• Vertically compress by a factor of 5.• Shift up 7 units.O A. g(x) = } (x+7)O B. g(x) = 5x + 7O c. g(x) = 5x - 7O D. g(x) = 5x+7

Answer 1

The rules for transforming a function f(x) into a function g(x) are:

g(x) = a·f(b(x-c)) + d where:

a = vertical cmpress (stretch)

b = horizontal dilation (stretch)

c = horizontal (left/right) shift

d = vertical (up/down) shift

`\begin{gathered} For\text{ F(x) = x} \\ g(x)\text{ = a.f(b(x-c))+d} \end{gathered}`
`a\text{ = }(1)/(5)\text{ , b = 1 , c = 0 }`

Shift up 7 units means d = +7

`g(x)\text{ = }(1)/(5)x+7`

Hence the correct answer is Option D