Exploring Exponential Functions

An exponential function is a function where x is the exponent. A basic exponential function is y = 2^x. Using a graphing application, like Desmos.com, graph y = 2^x. Sketch the graph below.

1. Select all phrases that fit the graph of y = 2^x. (Hint: 8 should be selected).

curve	straight	y-intercept = 1	positive x-values
positive y-values	negative x-values	point (2, 1)	x-intercept = 0
decreasing	y-intercept = 0	no y-intercept	negative y-values
no x-intercept	increasing	x-intercept = 1	point (1, 2)

General form: y = a*2^(x-h) + k

The general form of an exponential function allows for changes to the basic function y = 2^x. These changes follow specific patterns. Now we will focus on how these different changes affect the basic graph of y = 2^x.

Effect ofk

2. In a graphing program, graph the following 3 functions in the same coordinate plane.

1. y = 2^x
2. y = 2^x+ 3
3. y = 2^x- 2

3. How doesk (+3 and -2 in functions b & c) change the exponential graph? Select the best description from the words below. (Hint: one fits)

compresses-fatter	shifts right/left	reflects over x-axis
shifts up/down	stretches-steeper	reflects over y-axis

Effect ofh

4. In a graphing program, graph the following 3 functions in the same coordinate plane.

1. y = 2^x
2. y = 2^{x+ 3}
3. y = 2^x-2

5. How doesh (+3 and -2 in functions b & c) change the exponential graph? (Hint - see choices from k section)

Effect ofa

6. In a graphing program, graph the following 4 functions in the same coordinate plane.

1. y = 2^x
2. y =3*2^x
3. y =0.5*2^x
4. y =-2*2^x

7. How doesa change the exponential graph? (Hint - see choices from k section)

8. Exponential functions do exist with bases other than 2. Graph the following functions. Note - enter y = (-2)^x with the parentheses as shown.

1. y = 4^x
2. y = (0.5)^x
3. y = (-2)^x

9. Describe some differences in the three functions from those you have previously graphed.