AnswersAZ-Common Core Algebra II BLinear Growth vs. Exponential Growth

Linear Growth vs. Exponential Growth — Unit test Answers

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1
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A coordinate plane with a line passing through (negative 4, 3), (0, 1), and (4, negative 1).

Question illustration
f
f(x) = –2x + 1
f
f(x) = –x + 1
Option f
f
f(x) = x + 1
Option f
f
f(x) = 2x + 1
2
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What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?

A
Option
Option A
B
Option
Option B
C
3
D
6
3

An exponential growth function has an asymptote of y = –3. Which might have occurred in the original function to permit the range to include negative numbers?

A
A whole number constant could have been added to the exponential expression.
B
A whole number constant could have been subtracted from the exponential expression.
C
A whole number constant could have been added to the exponent.
D
A whole number constant could have been subtracted from the exponent.
4

Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?

Question illustration
f
f(x) = x + 4
Option f
f
f(x) = x + 6
Option f
f
f(x) = x – 10
Option f
f
f(x) = x – 12
Option f
5

The graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.

Question illustration
A
$1.50
B
$2.00
C
$2.50
D
$3.00
6

The table represents a linear equation.

Question illustration
A
y – 6 = (x – 2)
Option A
B
y – 6 = (x – 2)
Option B
C
y + 6 = (x + 2)
Option C
D
y + 6 = (x + 2)
Option D
7

A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the number of calories, numbered 3 to 27. A straight line with a positive slope begins at point (0, 0) and ends at point (6.8, 27).

Question illustration
A
Each strawberry contains 4 calories.
B
Each strawberry contains 3 calories.
C
Twenty-four strawberries contain 6 calories.
D
Four strawberries contain 15 calories.
8

A graph titled Cost of Erasers. The x-axis shows the number of erasers, numbered 1 to 9, and the y-axis shows the total cost in dollars, numbered 0.5 to 4.5. Blue diamonds appear at points (1, 0.5), (2, 1), (3, 1.5), (4, 2), (5, 2.5), (6, 3), (7, 3.5), (8, 4), (9, 4.5).

Question illustration
A
Each eraser costs $1.00.
B
Each eraser costs $1.50.
C
Three erasers cost $6.
D
Seven erasers cost $3.50.
9

Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?

(
(2, 12)
(
(2, 18)
(
(2, 7)
(
(3, 7)
10

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?

A
y = –3x
B
y = –
Option B
C
y =
Option C
D
y = 3x
11

Over which interval does the exponential show a more rapid rate of change?

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

A line is drawn through (–4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?

A
The line represents a direct variation because = .
Option A
B
The line represents a direct variation because it is horizontal.
C
The line does not represent a direct variation because it does not go through the origin.
D
The line does not represent a direct variation because –4(3) ≠ 4(3).
13

Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of granola that costs $2.00 per pound. The walnuts cost $6 per pound. He uses the equation to represent the total cost, where x represents the number of pounds of granola and y represents the number of pounds of walnuts. He solves the equation for y, the number of pounds of walnuts he can buy. Which is the first error that Tomas made?

Question illustration
A
Tomas substituted the 3 for x when he should have substituted 6 for x.
B
Tomas added 6 to both sides of the equation instead of subtracting 6.
C
Tomas should have written the equation as .
Option C
D
Tomas substituted 3 for x when he should have substituted 3 for y.
14

Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lb. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?

A
3x – 10y = 50
B
3x = 50 – 10y
C
50 + 10y = 3y
D
50 + 3y = 10y
15

Which is the graph of ?

Question illustration
A
Option
B
Option
C
Option
D
Option
16

The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of . Which shows the graph of this equation?

Question illustration
A
Option
B
Option
C
Option
D
Option
17

A coordinate plane with a horizontal line passing through (negative 3, negative 3), (negative 3, 0) and (negative 3, 3).

Question illustration
A
The value of A can be –1 if the value of C is 3 and the value of B is 0.
B
The value of A can only be 1, the value of C can only be –3, and the value of B is 0.
C
The standard form of the equation can be shown as 3x = –9.
D
The standard form of the equation can only be x + 3 = 0.
18

The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of . Which shows the graph of this equation?

Question illustration
A
Option
B
Option
C
Option
D
Option
19

A coordinate plane with a line passing through (negative 4, 3), (0, 1), and (4, negative 1).

Question illustration
A
f(x) = –2x + 1
B
f(x) = –x + 1
Option B
C
f(x) = x + 1
Option C
D
f(x) = 2x + 1
20

The graph of an exponential function and a linear function are shown below. Exponential Linear Which statement is true about the functions?

Question illustration
A
The exponential function is generally growing slower than the linear function.
B
The exponential function is generally growing faster than the linear function.
C
The linear function is generally growing faster than the exponential function.
D
The exponential function and the linear function are generally growing at the same rate.

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