Exercise 6 Page 275

Let's graph and describe the domain and range of the given function first. Then we will compare the graph to the graph of the parent function.

Graphing and Describing the Domain and Range

To graph the given exponential function, we will first make a table of values.

x	2(1/4)^x	f(x)=2(1/4)^x
- 1	2(1/4)^(- 1)	8
0	2(1/4)^0	2
1	2(1/4)^1	0.5
4	2(1/4)^4	≈ 0.0078

Let's now plot and connect the points ( - 1, 8), ( 0, 2), ( 1, 0.5), and ( 4, 0.0078) with a smooth curve.

We can see in the graph that the range is all real numbers greater than zero. The domain of exponential functions is all real numbers. Domain:& All real numbers Range:& y>0

Comparing the Graph to the Parent Function

The parent function is g(x)=( 14)^x. Let's graph it on the same coordinate plane. To do it, we will make a table of values first.

x	( 14)^x	g(x)=( 14)^x
- 1.5	( 14)^(- 1.5)	8
- 1	( 14)^(- 1)	4
0	( 14)^0	1
4	( 14)^4	≈ 0.004

Let's now plot and connect the points ( - 1.5, 8), ( - 1, 4), ( 0, 1), and ( 4, 0.004) with a smooth curve.

We can tell that the graph of f is a vertical stretch by a factor of 2 of the graph of g. The y-intercept of the graph of f, 2, is above the y-intercept of the graph of the parent function, 1.