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) I n the interactive figure, the graph of f (x) = c · a^x−h + k is drawn. 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 a from 2 to 4. Note the points on the graph.

(i) T he graph of f (x) = 2^x contains the points (−1,___ ) , (0,___ ) , and (1,____ )

(ii) T he graph of f ( x) = 3x contains the points (−1,_____ ) , (0,_____ ) , and (1,_____ )

(b) Check the “Show Reciprocal of Base a ” box. The graph ofis drawn. 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 a from 2 to 4. Note the points on the graph.

(i) The graph of g (x) = (1/2)^x contains the points (−1, ) , (0,____ ) , and (1,____ )

(ii) The graph of g (x) = (1/3)^x contains the points (−1,____ ) , (0,____ ) , and (1,____ )

(c) The graph of g (x) = (1/a)^x is a reflection about the______ ( x -axis/ y -axis/origin) of the graph of f ( x) = a x , a > 1.

(d) I n the graph of f (x) = a^x with 0 x with a > 1, the graph is______ (increasing/decreasing) over its domain.

(e) Uncheck the “Show Reciprocal of Base a ” box. Use the sliders to set the value of c to 1, a to 1, h to 0, and k to 0. What type of graph is f (x) = 1^x ? Explain why a ≠ 1 is an exponential function.

Transcribed Image Text:

x-h of g(x) = c. · (²) * + k