Question

What function is vertically stretched by a factor of 3 and translated 4 units right from the parent function

A. log_(5) (3x+4)
B. 3log_(5) (x-4)
C. 3(5^x+4)
D. 5^3x-4

Answer 1

Option B is right

Explanation:

Consider the parent function

`y=log_5 x`

When we stretch by a factor of 3 we get the transformed funciton as

`y=3log_5 x`

Next is horizontal shift to the right by 4 units

This will be done when x is replaced by x-4

Hence we get correct answer as

`y=3log_5 (x-4)`

Option B is right

Answer 2

The correct answer is:

B) 3log₅(x-4).

Explanation:

To stretch a function by a factor of 3, we multiply the function by 3. This eliminates A and D.

To translate a function 4 units right, we add -4 to the variable before anything else is applied to it; this eliminates C.

In choice B, the log function is multiplied by 3, which gives us our vertical stretch; and the x is subtracted by 4 before anything else is applied to it, so it is translated 4 units right.