AnswersHigh School Math 2 ALinear Growth vs. Exponential Growth

Translations of Exponential Functions Answers

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Which exponential function has an initial value of 2?

A
f(x) = 2(3x)
B
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (2, 2).
Option B
C
f(x) = 3(2x)
D
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.
Option D
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A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 12.5, 2.5, 0.5, 0.1, 0.02.

Question illustration
A
f(x) = 0.2(0.5x)
B
f(x) = 0.5(5x)
C
f(x) = 0.5(0.2x)
D
f(x) = 0.2(0.2x)
3

Which graph represents a function with an initial value of ?

Question illustration
A
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.08), (0, 0.4), (1, 2).
Option A
B
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.1), (0, 0.5), (1, 2.5).
Option B
C
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.4), (0, 0.2), (1, 1).
Option C
D
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.12), (0, 0.6), (1, 3).
Option D
4

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 1.5), (0, 3), (1, 6).

Question illustration
A
f(x) = 2(3x)
B
f(x) = 3(3x)
C
f(x) = 3(2x)
D
f(x) = 2(2x)
5

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 1).

Question illustration
A
f(x) = 2(6)x
B
f(x) = (6)x
Option B
C
f(x) = 2
Option C
D
f(x) =
Option D
6

The graph shows f(x) = and its translation, g(x).

Question illustration
A
translation of four units up
B
translation of five units up
C
translation of four units to the right
D
translation of five units to the right
7

The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.

Question illustration
A
g(x) = 5x – 9
B
g(x) = 5x – 10
C
g(x) = 5x – 9
D
g(x) = 5x – 10
8

Which is the graph of g(x) = (0.5)x + 3 – 4?

A
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, negative 4).
Option A
B
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 3. It crosses the y-axis at (0, 3).
Option B
C
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, 4).
Option C
D
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 4. It crosses the y-axis at (0, 12).
Option D
9

The graphs of f(x) = 10x and its translation, g(x), are shown.

Question illustration
A
g(x) = 10x – 3
B
g(x) = 10x + 3
C
g(x) = 10x – 3
D
g(x) = 10x + 3
10

Which steps will translate f(x) = 3x to g(x) = 3x + 1 + 4?

A
Shift f(x) = 3x one unit up and four units to the right.
B
Shift f(x) = 3x one unit up and four units to the left.
C
Shift f(x) = 3x one unit to the right and four units up.
D
Shift f(x) = 3x one unit to the left and four units up.

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