4.3.3 Graphing Exponential Functions Day 1 Handout (AAL)

1. Examine each table of values and determine which table(s) represent an exponential function.
   1. b) c) d)

2. For each exponential function below,

1. state the equation of the asymptote.
2. state the y-intercept.
3. sketch the curve.

a) y = 2 ^x + 1

b) y = 3(2) ^x − 2

c) y = −2(2) ^x + 3

d) ƒ (x) = −4(2) ^x + 5

e) y = 3^x −1

i) y = −2(4) ^x + 3

f) y = −3^x − 1

j) ƒ (x) = 5^x

g) ƒ (x) = 2(3) ^x + 1

k) y = 0.5(2) ^x + 1

h) y = 4(3) ^x

l) ƒ (x) = −1.5(3) ^x − 1

3. State the domain and range for the following functions.
   1. y = 4 ^x
   2. y = 2 ^x − 3

c) y = −4(3) ^x + 5

d) y = −2 ^x

4. Determine the exponential function, in the form y = a(2) ^x + c , that represents each graph below.

5. Determine the exponential function, ƒ (x) = a(b) ^x + c , that represents each graph below.

x	y		x	y		x	y		x	y
1	-2		-2	4		-3	12		0	1
2	-6		-1	12		-2	18		1	2
3	-18		0	24		-1	24		2	4
4	-54		1	48		0	30		3	8
5	-162		2	144		1	36		4	16

6. Match each function on the graph with the equations below.

1. y = 2 ^x − 6

b) y = 10 ^x − 6

⎛ 3 ⎞ ^x

c) y = ⎜ ⎟ − 6

⎝ 2 ⎠

d) y = 4 ^x − 6

Answers

1. a (multiplier of 3), and d (multiplier of 2).

2. a) 5

2. 5
3. d)

−5 5 −5 5

−5 −5

f) 5 g) h)

−5 5

−5

j) k) l)

3. a) D: {x | x∈R} b) D: {x | x∈R} c) D: {x | x∈R} d) D: {x | x∈R}

R: {y | y > 0, y∈R} R: {y | y > -3, y∈R} R: {y | y < 5, y∈R} R: {y | y < 0, y∈R}

4. a)
5. a)

y = 2 ^x − 3

ƒ (x) = 2(2) ^x

b) y = −3(2) ^x + 4

b) ƒ (x) = 2(3) ^x − 4

c) y = 3(2) ^x

c) ƒ (x) = −(3) ^x + 5

d) y = −(2) ^x + 2

4. ƒ (x) = 5^x

a) III b) I c) IV d) II