Question

Function is a transformation of the parent exponential function, (6(x) = 2^x), (h(t) = -3.2^t". Which statement is true?

a) Function h is a horizontal translation of function f.
b) 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

Function h is a reflection and a dilation of function f, confirmed by the presence of a negative sign and a scalar multiple in its equation.

Step-by-step explanation:

The function h(t) = -3 · 2^t is compared to the parent exponential function f(x) = 2^x to determine its transformation. The negative sign in front of 3 in h(t) indicates a reflection across the x-axis, and the presence of the scalar 3 is a dilational transformation that stretches the graph by a factor of 3 in the y-direction. Therefore, the correct statement is (c) Function h is a reflection and a dilation of function f. There are no translations involved because the exponent t is not altered by an addition or subtraction of a constant.