Question

Instructions: For the function given, determine the direction and amount of vertical shift from the function =(2).

Answer 1

SOLUTION

From the translation given, the amount of vertical shift is 3 units down

This was derived from -3

Hence the answer is 3 units down

Answer 2

The function is translated 1 unit to the left, 3 units down, and is stretched by a factor of 6.

Translated functions use their principle (original) function and add lateral and vertical changes to the function. The principle function is y=(2)^x. Therefore, adding one to that x-value would shift it to the left by 1 unit for every x-value. NOTE: +1 is actually to the right, but transformations reverse that, so it is actually to the left towards the negative domains. The entire function is shifted down 3 units; the “-3” as the last term is subtracting the entire function, so the y-coordinates will all shift down 3 units. And the “a” value of the function is 6. When a>0, the function stretches. So, the function will stretch by a factor of 6, since it is multiplying the entire range of the function.