Question

Select all the correct statements. (For this problem, assume that an exponential function is of the form kaˣ, where a > 0.)

(A) If the graph of an exponential function is reflected in the x axis, then we obtain the graph of another exponential function.
(B) If the graph of an exponential function is reflected in the y axis, then we obtain the graph of another exponential function.
(C) If the graph of an exponential function is translated vertically, then we obtain the graph of another exponential function.
(D) If the graph of an exponential function is translated horizontally, then we obtain the graph of another exponential function.

Answer 1

An exponential function of the form kaˣ, where a > 0, can be reflected in the x-axis, y-axis, or translated vertically to obtain another exponential function. However, horizontal translation does not result in another exponential function.

Step-by-step explanation:

For an exponential function of the form kaˣ, where a > 0, the correct statements are:

1. (A) If the graph of an exponential function is reflected in the x-axis, then we obtain the graph of another exponential function. When the function is reflected in the x-axis, the sign of x changes, but a remains the same, resulting in another exponential function.
2. (B) If the graph of an exponential function is reflected in the y-axis, then we obtain the graph of another exponential function. When the function is reflected in the y-axis, the sign of a changes, but x remains the same, resulting in another exponential function.
3. (C) If the graph of an exponential function is translated vertically, then we obtain the graph of another exponential function. When the function is translated vertically, the constant k changes, but a and x remain the same, resulting in another exponential function.
4. (D) If the graph of an exponential function is translated horizontally, then we obtain the graph of another exponential function. This statement is incorrect since horizontal translation changes the value of x and therefore does not result in another exponential function.