Open the “Exponential Functions” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.

(a) Use the sliders to set the value of c to 1, a to 2, h to 0, and k to 0. Now, use the slider to increase the value of h from 0 to 4. The graph shifts_______ (horizontally/ vertically) h units_________ (left/right/up/down).

(b) Use the sliders to set the value of c to 1, a to 2, h to 0, and k to 0. Now, use the slider to decrease the value of h from 0 to −4.

(i) What is the equation of the function when h = −3?

(ii) As h decreases from 0 to −4, the graph shifts________ (horizontally/vertically) h units______ (left/right/up/down).

(c) Use the sliders to set the value of c to 1, a to 2, h to 0, and k to 0. Now, use the slider to increase the value of k from 0 to 4. The graph shifts______ (horizontally/ vertically) h units____ (left/right/up/down).

(d) Use the sliders to set the value of c to 1, a to 2, h to 0, and k to 0. Now, use the slider to decrease the value of k from 0 to −4.

(i) What is the equation of the function when k = −3?

(ii) What is the horizontal asymptote when k = −3?

(iii) As k decreases from 0 to −4, the graph shifts______ (horizontally/vertically) k units_____ (left/right/up/down).

(e) Use the sliders to set the value of c to 1, a to 2, h to 0, and k to 0. Now, use the slider to increase the value of c from 1 to 4. The graph is vertically________(stretched/compressed) by a factor of c. When c = 2, the points (−1,____), (0,_____), and (1,_____) are on the graph of f.

(f) In the graph of f ( x) = c · 2^x with c < 0, the graph is________ (increasing/decreasing) over its domain.