AnswersAISD Algebraic Reasoning A Credit Recovery 2026-2027Modeling Functions Using Finite Differences

Reflections of Exponential Functions Answers

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1
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Which is the range of the function f(x) =(9)x?

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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
2
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Which graph represents a reflection of f(x) = (10)x across the y-axis?

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A
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, negative 1).
Option A
B
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1).
Option B
C
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 1).
Option C
D
On a coordinate plane, an exponential function increases from quadrant 3 to quadrant 4 and approaches y = 0. It goes through (negative 1, negative 1).
Option D
3

On a coordinate plane, 2 exponential functions are shown. f (x) decreases from quadrant 2 to quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 4) and goes through (1, 2). g (x) increases from quadrant 3 into quadrant 4 and approaches y = 0. It crosses the y-axis at (0, negative 4) and goes through (1, negative 2).

Question illustration
A
g(x) = −4(2)x
B
g(x) = 4(2)−x
C
g(x) = −4
Option C
D
g(x) = 4
Option D
4

The function g(x)=8(4x) is reflected across the x-axis to create f(x).

Question illustration
A
f(x)=8(4)x
B
f(x)=−8(4)x
C
f(x)=8
Option C
D
f(x)=−8
Option D
5

How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?

A
g(x) is the reflection of f(x) over the x-axis.
B
g(x) is the reflection of f(x) over the y-axis.
C
g(x) is the reflection of f(x) over both axes.
D
g(x) and f(x) will appear to be the same function.
6

On a coordinate plane, 2 exponential functions are shown. Function f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 0.5) and goes through (1, 4). Function g (x) approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.5) and goes through (1, negative 4).

Question illustration
A
g(x) = (10)x
Option A
B
g(x) =
Option B
C
g(x) =
Option C
D
g(x) = (10)-x
Option D
7

The graph of f(x) = 6(0.25)x and its reflection across the y-axis, g(x), are shown.

Question illustration
A
all real numbers
B
all real numbers less than 0
C
all real numbers greater than 0
D
all real numbers greater than or equal to 0
8

Which is the domain of the function f(x) = ?

Question illustration
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
9

On a coordinate plane, 2 exponential fuctions are shown. Function f (x) decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 6) and goes through (1, 2). Function g (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 2) and crosses the y-axis at (0, 6).

Question illustration
A
g(x) = −6
Option A
B
g(x) = −6
Option B
C
g(x) = 6(3)x
D
g(x) = 6(3)−x
10

Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?

A
On a coorindate plane, an exponential function starts in quadrant 3 and increases and approaches y = 0 in quadrant 4. It crosses the y-axis at (0, 6) and goes through (1, negative 3).
Option A
B
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and crosses the y-axis at (0, 6).
Option B
C
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (negative 1, negative 3) and crosses the y-axis at (0, negative 6).
Option C
D
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in the first qudrant. It goes through the y-axis at (0, 6) and goes through (1, 3).
Option D

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