AnswersOKCPS FY24 Algebra II S1Combining Functions

Combining Functions — Unit test Answers

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1
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The graph of f(x) is shown below.If g(x) and f(x) are inverse functions, which graph represents g(x)?

Question illustration
A
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up sharply through (2, 4).
Option A
B
On a coordinate plane, a curve opens down and to the left in quadrant 2. The curve starts at (0, 0) and gradually curves through (negative 4, 2).
Option B
C
On a coordinate plane, a curve opens open and to the left in quadrant 3. The curve starts at (0, 0) and curves gradually through (negative 4, negative 2).
Option C
D
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up through (4, 1).
Option D
2
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Which statement verifies that f(x) and g(x) are inverses of each other?

A
Option
Option A
B
and
Option B
C
Option
Option C
D
and
Option D
3

f(x) = 2x – 1g(x) = 7x – 12What is h(x) = f(x) + g(x)?

A
h(x) = 9x – 13
B
h(x) = 9x – 12
C
h(x) = –5x + 11
D
h(x) = 5x – 13
4

For what value of is the function one-to-one?

Question illustration
A
2
B
5
C
11
D
13
5

One vendor at a craft fair wants to earn $1,200 selling various items over a weekend. The following function can be used to model the average selling price of x number of items. The mathematical domain of this function is all real numbers except 0.

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A
The reasonable domain is limited to positive whole numbers.
B
The reasonable domain is limited to positive rational numbers.
C
The reasonable domain is limited to whole numbers greater than 1,200.
D
The reasonable domain is limited to rational numbers greater than 1,200.
6

Consider the table of values for .

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

The dimensions of various-sized mirrors are created using the expression 0.5x – 2 for the width and 2x + 2 for the length. The maximum length of the mirrors is 52 centimeters.

A
mathematical: reasonable:
Option A
B
mathematical: reasonable:
Option B
C
mathematical: reasonable:
Option C
D
mathematical: reasonable:
Option D
8

The function f(x) = 2.5x + 75 is used to model the cost of renting billboard space depending on the area, in square feet, of the billboard, x, and including a standard layout fee. The mathematical range for the function is the set of real numbers.

A
The reasonable range contains only integers.
B
The reasonable range contains only positive rational numbers.
C
The reasonable range contains only integers greater than 75.
D
The reasonable range contains only positive rational numbers greater than 75.
9

Which function is the inverse of ?

Question illustration
A
f Superscript negative 1 Baseline (x) = negative one-fifth x + four-fifths
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

The width of a rectangle is modeled by the function w(x) = 3x – 6, and the length of the rectangle is modeled by the function l(x) = 5x + 7.How can the functions be combined to find a function, a(x), that models the area of the rectangle?

A
a(x) = 8x + 1
B
a(x) = 16x + 2
C
a(x) = 15x2 – 9x – 42
D
a(x) = 30x2 – 18x – 84
11

The area of a trapezoid can be found using the formula , where B(x) is the sum of the bases and h(x) is the height.Which graph could include the functions?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

Which graph represents the same relation as the set ?

Question illustration
A
A coordinate plane has 3 points. The points are (negative 3, 2), (3, negative 2), (5, 5).
Option A
B
A coordinate plane has 4 points. The points are (negative 3, 2), (3, negative 2), (3, 3), (5, 5).
Option B
C
A coordinate plane has 7 points. The points are (negative 3, 0), (0, 5), (0, 3), (0, 2), (0, negative 2), (3, 0), (5, 0).
Option C
D
A coordinate plane has 4 points. The points are (negative 2, 3), (2, negative 3), (3, 3), (5, 5).
Option D
13

Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns 1.5% a year. Jack opens his account with $1,000, and Susie opens her account with $800. x = number of yearsThe following functions represent the value of the savings accounts in x years:Jack’s savings account: f(x) = 1000(1.015)xSusie’s savings account: g(x) = 800(1.015)x Which function represents the total amount Jack and Susie will save in x years?

A
200(1.015)x
B
1800(1.015)x
C
1800(1.015)2x
D
1800(1.030)x
14

Which relation below represents a one-to-one function?

A
A 2-column table has 5 rows. The first column is labeled x with entries 5, 14, 7, 13, 12. The second column is labeled f (x) with entries 26, 197, 50, 170, 197.
Option A
B
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 5, 2, 1, 2, 5.
Option B
C
A 2-column table has 5 rows. The first column is labeled x with entries 7.25, 7.5, 7.75, 8, 8.5. The second column is labeled f (x) with entries 11, 13, 15, 13, 11.
Option C
D
A 2-column table has 5 rows. The first column is labeled x with entries 9, 2, 4, 1, 5. The second column is labeled f (x) with entries 12, 7, 9, 13, 5.
Option D
15

One cattle farmer plans to grow his cattle population 2% each year, modeled by the function f(t) = 100(1.02)t. Another farmer intends to add 20 cattle per year, modeled by the function g(t) = 100 + 20t.For this application, the domain is restricted to t ≥ 0. If the farmers become partners, which function represents the total cattle they will have after t years?

A
h(t) = 200(21.02)t
B
h(t) = 200(20.4)t
C
h(t) = 100(1.02)t + 20t + 100
D
h(t) = 2,000t(1.02)t + 100

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