AnswersAlgebra III ALinear Piecewise Defined Functions

Linear Piecewise Defined Functions — Unit test Answers

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A function, h(x), is defined as shown.h(x) = Which graph represents h(x)?

Question illustration
A
Option
B
Option
C
Option
D
Option
2
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Which graph represents the function f(x) = |x| – 4?

A
On a coordinate plane, an absolute value graph has a vertex at (0, 4).
Option A
B
On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0).
Option B
C
On a coordinate plane, an absolute value graph has a vertex at (0, negative 4).
Option C
D
On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Option D
3

On a coordinate plane, an absolute value graph has a vertex at (1, 3).

Question illustration
A
g(x) = |x + 1| + 3
B
g(x) = |x + 3| – 1
C
g(x) = |x – 1| + 3
D
g(x) = |x + 3| + 1
4

If f(x) = − 5, what is f(8.6)?

Question illustration
A
3
B
4
C
8
D
9
5

The step function f(x) is graphed.

Question illustration
A
0
B
1
C
2
D
4
6

The graph of a function is shown.

Question illustration
A
f(x) =
Option A
B
f(x) =
Option B
C
f(x) =
Option C
D
f(x) =
Option D
7

The graph of the step function g(x) = –⌊x⌋ + 3 is shown.

Question illustration
A
{x| x is a real number}
B
{x| x is an integer}
C
{x| –2 ≤ x < 5}
D
{x| –1 ≤ x ≤ 5}
8

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.f(x) = Which describes the meaning of f(x)?

Question illustration
A
A customer earns 1 free night per 10 nights stayed.
B
A customer starts with 1 free night and then earns another free night after every 10 nights stayed.
C
A customer earns x – 10 free nights for every 10 nights stayed.
D
A customer earns 10 free nights after x number of nights stayed.
9

The function f(x) is to be graphed on a coordinate plane.f(x) = At what point should an open circle be drawn?

Question illustration
A
(–1, 0)
B
(0, 0)
C
(0, 1)
D
(1, 0)
10

Which graph represents the function p(x) = |x – 1|?

A
Option
B
Option
C
Option
D
Option
11

Which could be the graph of f(x) = |x - h| + k if h and k are both positive?

A
Option
B
Option
C
Option
D
Option
12

A piecewise function is represented by the graph below.

Question illustration
A
x < –1
B
–1 ≤ x ≤ 1
C
1 ≤ x < 2
D
x > 1
13

What is the range of the function g(x) = |x – 12| – 2?

A
{y | y > –2}
B
{y | y > –2}
C
{y | y > 12}
D
{y | y > 12}
14

The function h(x) is defined as shown.h(x) =

Question illustration
A
–∞ < h(x) < ∞
B
h(x) ≤ 5
C
h(x) ≥ 5
D
h(x) ≥ 3
15

The graph represents f(x) = .

Question illustration
A
-2
B
0
C
1
D
2
16

The graph represents y = ⌈x⌉ + 1.

Question illustration
A
–5
B
–4
C
–2
D
–1
17

A clothing store uses the step function f(x) to recommend jeans sizes as a function of x, a child’s height in inches.f(x) = According to the function, which is the height of a child who should wear size 2 jeans?

Question illustration
A
41.9 inches
B
42 inches
C
44 inches
D
44.1 inches
18

The cost of a single ticket depends on the number of tickets, t, purchased in a group, as represented by the function C(t).C(t) = What is the total cost for 20 tickets?

Question illustration
A
$14.50
B
$16.00
C
$290.00
D
$320.00
19

Which functions have a vertex with a x-value of 0? Select three options.

A
f(x) = |x|
B
f(x) = |x| + 3
C
f(x) = |x + 3|
D
f(x) = |x| − 6
E
f(x) = |x + 3| – 6
20

The piecewise function f(x) has opposite expressions.f(x) = Which is the graph of f(x)?

Question illustration
A
Option
B
Option
C
Option
D
Option

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