Question

Function h is a transformation of the parent exponential function, f(x) = 2* h(t) = -3.24

Which statement is true?
A Function h is a horizontal translation of function f.
В. Function h is a vertical translation of function f.
C. Function h is a reflection and a dilation of function f.
D Function h is a reflection and a translation of function f.

Answer 1

The function h(t) = -3.24 is a reflection and a dilation of the parent function f(x) = 2^x, resulting in a constant value which represents a horizontal line.

Step-by-step explanation:

To determine which statement about the function h(t) = -3.24 is true in relation to the parent exponential function f(x) = 2x, we must analyze the given transformation. The given function h(t) has a negative constant value, which indicates that it does not depend on t and is a horizontal line. Comparing this with the parent function, we can conclude that the transformation from f(x) to h(t) involves flipping the graph over the x-axis (since the result is negative) and squashing it down to a constant value.

Reflecting over the x-axis is a reflection transformation, while changing the size of the graph is known as dilation. Therefore, the correct answer is C: Function h is a reflection and a dilation of function f.