Question

Let g be a vertical shrink by a factor of 1/3 followed by a translation 3 units right

of the graph of f(x) = srqt of x + 5.

Answer 1

g(x) = (
`√(x-3)`)/3 + 5

Explanation:

f(x) =
`√(x)` + 5

`√(x)` + 5 ==> 1/3 *
`√(x)` + 5 ==> vertical shrink is when the function's y-coordinates shrink from the y-intercept (5 is the y-int) by a factor of 1/3

`√(x)`/3 + 5 ==>(
`√(x-3)`)/3 + 5 ==> in order to translate the graph 3 units to the right, subtract x by 3 since x is being affected when the graph moves left/right. In addition, x now has to be 3 units greater in order for the function to have the same value:

`√(4-3)` =
`√(1)`

4 > 1 and 4 = 1 + 3

Hence, g(x) = (
`√(x-3)`)/3 + 5