Exponential Models
Question 1 Objective: Graph and analyze geometric sequences as a special case of exponential functions with the
domain restricted to natural numbers.
Which explains why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve?
A. The range contains only natural numbers.
B. The domain contains only natural numbers.
C. Exponential bases must be whole numbers.
D. Initial values must be whole numbers.
Question 2 Objective: Graph and analyze geometric sequences as a special case of exponential functions with the
domain restricted to natural numbers.
Which is the graph of the sequence defined by the function f(x) = 100(0.5)x - 1?
A
B
C
D
Question 3 Objective: Graph and analyze geometric sequences as a special case of exponential functions with the
domain restricted to natural numbers.
Which is the graph of the sequence defined by the function f(x + 1) = 3/5f(x) when the first term in the sequence is 375?
A
B
C
D
Question 4 Objective: Graph and analyze geometric sequences as a special case of exponential functions with the
domain restricted to natural numbers.
The second and fourth terms of a geometric sequence are shown on the graph.
Which function can be used to model the sequence?
f(x) = 1,200
f(x) = 1,200
f(x) = 1,500
f(x) = 1,875
Question 5 Objective: Graph translations of exponential functions.
Which is the graph of g(x) = (2/3)X– 2?
B
C
A
D
Question 6 Objective: Graph translations of exponential functions.
The table represents ordered pairs that satisfy two exponential functions, f(x) and g(x).
If f(x) = 5x, which statements about f(x) and g(x) are true? Check all that apply.
A. g(x) = 5x – 8
B. g(x) = 5x + 8
C. The graph of g(x) is the result of translating the graph of f(x) eight units up.
D. The graph of g(x) is the result of translating the graph of f(x) eight units to the left.
E. The graph of g(x) is the result of translating the graph of f(x) eight units to the left and eight units up.
Question 7 Objective: Analyze key aspects of exponential functions that have been translated.
What are the domain and range of f(x) = (1/6)X + 2?
A. domain:
; range: {y | y > 0}
C. domain: {x | x is a real number}; range: {y | y > 2}
B. domain:
; range: {y | y > 2}
D. domain: {x | x is a real number}; range: {y | y > –2}
Question 8 Objective: Analyze key aspects of exponential functions that have been translated.
f(x) = (2/5)X
g(x) = (2/5)X – 3
Which statement about f(x) and its translation, g(x), is true?
A. The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
B. The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
C. The asymptote of g(x) is the asymptote of f(x) shifted three units down.
D. The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Question 9 Objective: Graph reflections of exponential functions.
The function f(x) = 8(1/4)X is reflected across the y-axis to create g(x). Which table of values could be used to graph g(x)?
B
A
C
D
Question 10 Objective: Analyze key aspects of exponential functions that have been reflected across an axis.
The graph of f(x) = ½ (2.5)x and its reflection across the x-axis, g(x), are shown.
What is the range of g(x)?
A. All real numbers
B. All real numbers less than 0
C. All real numbers greater than 0
D. All real numbers less than or equal to 0
Question 11 Objective: Analyze key aspects of exponential functions that have been reflected across an axis.
An exponential function f(x) is reflected across the x-axis to create the function g(x). Which is a true statement
regarding f(x) and g(x)?
A. The two functions have the same initial value.
B. The two functions will cross each other on the axis.
C. The two functions have reciprocal output values of each other for any given input value.
D. The two functions have opposite output values of each other for any given input value.
Question 12 Objective: Determine the parameters and create an equation for a vertically dilated exponential growth or
decay function given a table, equation, or scenario.
Which is the initial value that shrinks an exponential growth function by 50%?
A. 1/5
B. ¼
C. 1/3
D. 1/2
Question 13 Objective: Determine the parameters and create an equation for a vertically dilated exponential growth or
decay function given a table, equation, or scenario.
Which value of a in the exponential function below would cause the function to shrink?
f(x) = a(3/2)X
A. 4/5
B. 5/4
C. 3/2
D. 7/4
Question 14 Objective: Determine the parameters and create an equation for a vertically dilated exponential growth or
decay function given a table, equation, or scenario.
Which is a stretch of an exponential growth function?
A. f(x) =
B. f(x) =
C. f(x) =
D. f(x) =
Question 15 Objective: Determine the parameters and create an equation for a vertically dilated exponential growth or
decay function given a table, equation, or scenario.
Iliana measured the shrinkage of the height of a snow bank over time. After the first day, the 20-inch snow bank measured
only 15 inches. After two days, the snow bank measured 11.25 inches. After three days, the snow bank measured only
8.4375 inches. Iliana wrote an equation to represent the exponential decay of the snow bank.
What exponential growth function did Iliana write?
A. f(x) = 20
B. f(x) = 20
C. f(x) =
(20x)
D. f(x) =
(20x)
Question 16 Objective: Identify an exponential decay function given tables, graphs, and function rules, determining the
rate of change. Which function represents exponential decay?
A. f(x) =
B. f(x) =
C. f(x) = 4
D. f(x) = 4
Question 17 Objective: Graph an exponential decay function, and state the domain and range.
Tanisha is graphing the function f(x) = 25(3/5)x. She begins by plotting the point (1, 15). Which could be the next point she
plots on the graph?
A. (2,9)
B. (2,-10)
C. (2, 14 2/5)
D. (2,5)
Question 19 Objective: Graph an exponential decay function, and state the domain and range.
Which is the graph of f(x) = 3/2 (1/3)x ?
A
B
C
D
Question 20 Objective: Identify an exponential growth function given tables, graphs, and function rules, determining the
rate of change. Which function represents exponential growth?
A. f(x) = 3x
B. f(x) = x3
C. f(x) = x + 3
D. f(x) = 3x
Question 21 Objective: Graph an exponential growth function, and state the domain and range.
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
A. (2,12)
B. (2,18)
C. (2,7)
D. (3,7)
Question 22 Objective: Write an exponential growth function to model a real-world problem, pointing out constraints in the
modeling context.
After 1 year, a bank account contains $7,746.90. After 2 years, the same account contains $7,901.84. Assuming no
deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account
after x years? (Round money values to the nearest penny.)
A. y = 7591.96(1.02)x
B. y = 7591.96(0.02)x
C. y = 7595(1.02)x
D. y = 7595(0.02)x
Question 23 Objective: Graph an exponential growth function, and state the domain and range.
Which is the graph of f(x) = 2(3)x?
A.
B.
C.
D.