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

Modeling Functions Using Finite Differences — Cumulative exam Answers

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1
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Choose the function that represents the data in the table.

Question illustration
A
y =
Option A
B
y = 2x – 3
C
y = 2x – 3
D
y = 2x2 – 3
2
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The function f(x) = –x2 – 4x + 5 is shown on the graph.

Question illustration
A
The domain of the function is all real numbers less than or equal to −2.
B
The domain of the function is all real numbers less than or equal to 9.
C
The range of the function is all real numbers less than or equal to −2.
D
The range of the function is all real numbers less than or equal to 9.
3

The table represents a linear function.

Question illustration
A
–8
B
–4
C
2
D
5
4

Choose the function that represents the data in the table.

Question illustration
A
y = x2
B
y = 3x2
C
y = x2 + 3
D
y = 2x + 3
5

Tanisha is graphing the function f(x) = 25()x. She begins by plotting the point (1, 15). Which could be the next point she plots on the graph?

Question illustration
A
(2, 9)
B
(2, –10)
C
(2, 14)
Option C
D
(2, 5)
6

Which table represents a linear function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. 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 = 7,746.90(1.02)x
B
y = 7,746.90(0.02)x
C
y = 7,595.96(1.02)x
D
y = 7,595.96(0.02)x
8

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

A
–15
B
–9
C
3
D
9
9

Which table represents a linear function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Select three options.

Question illustration
A
The vertex is the maximum value.
B
The axis of symmetry is x = .
Option B
C
The domain is all real numbers.
D
The range is all real numbers.
E
The function is decreasing from (−∞, 6.75).
11

Which is the graph of g(x) = – 2?

Question illustration
A
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, 2.25)
Option A
B
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, 0.44)
Option B
C
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
Option C
D
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)
Option D
12

The table shows the daily pay in dollars, f(x), earned by a salesperson who makes x number of sales.

Question illustration
A
f(x) = 50x2 + 200
B
f(x) = x50 + 200
C
Option
Option C
D
f(x) = 50x + 200
13

Which is the graph of ?

Question illustration
A
Option
B
Option
C
Option
D
Option
14

The graph of f(x) = (2.5)x and its reflection across the x-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 less than or equal to 0
15

Which function represents exponential growth?

A
f(x) = 3x
B
f(x) = x3
C
f(x) = x + 3
D
f(x) = 3x
16

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x + 5)3 − 6. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

A
(5, −6)
B
(−5, −6)
C
(5, 6)
D
(−5, 6)
17

What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?

A
(−4, 0) and (9, 0)
B
(4, 0) and (−9, 0)
C
(−3, 0) and (12, 0)
D
(3, 0) and (−12, 0)
18

Which is the graph of f(x) = 2(3)x?

A
Option
B
Option
C
Option
D
Option
19

Which is the graph of the function f(x) = x3 – x2 – 17x – 15?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long.

Question illustration
A
f(x) = x2 + 2x
B
Option
Option B
C
f(x) = 2x2
D
f(x) = 2x

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