Question

topic 4 review

1. write an example of an exponential function? answers will vary.
2. is this function an exponential growth of exponential decay?
3. what is the y intercept and the horizontal asymptote of the exponential function graphed above?
4. which of the following set of coordinate points contains the points used to represents the function $y=2^{x}$?

a.

x	-2	-1	0	1	2
y	.25	.5	0	2	4

b.

x	-2	-1	0	1	2
y	.25	.5	1	2	4

c.

x	-2	-1	0	1	2
y	4	2	1	2	4

d.

x	-2	-1	0	1	2
y	-4	-2	1	2	4

Explanation:

Step1: Define exponential function form

An exponential function has the form $y = a^x$ where $a>0, a
eq1$.

Step2: Identify decay from graph

Graph decreases as $x$ increases, so it is decay.

Step3: Find y-intercept from graph

Y-intercept is where $x=0$; graph crosses $(0,1)$.

Step4: Find horizontal asymptote

Graph approaches $y=0$ as $x\to\infty$.

Step5: Calculate $y=2^x$ for given x

For $x=-2$: $y=2^{-2}=\frac{1}{4}=0.25$; $x=-1$: $y=2^{-1}=0.5$; $x=0$: $y=2^0=1$; $x=1$: $y=2^1=2$; $x=2$: $y=2^2=4$.

Answer:

1. $y = 3^x$ (any valid exponential function is acceptable)
2. Exponential Decay
3. Y-intercept: $(0,1)$; Horizontal Asymptote: $y=0$
4. b.

x	-2	-1	0	1	2