Question

Describe the transformation of y = 2^x for the new function f(x) = 5(2^x) + 2.

a) The function is shifted 2 units up and vertically stretched by a factor of 5.
b) The function is shifted 2 units down and vertically stretched by a factor of 5.
c) The function is shifted 2 units up and horizontally compressed by a factor of 5.
d) The function is shifted 2 units down and horizontally compressed by a factor of 5.

Answer 1

The new function f(x) = 5(2^x) + 2 undergoes two transformations: a vertical stretch by a factor of 5 and a vertical shift upwards by 2 units, making option (a) the correct answer.

Step-by-step explanation:

When transforming the function y = 2^x to f(x) = 5(2^x) + 2, there are two separate transformations that occur:

Option (a) is the correct answer. The function is shifted 2 units up and vertically stretched by a factor of 5.