AnswersMathematics IIIMathematical Modeling: Part Three

Practice Test Answers

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1
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Which of the following is the graph of f of x is equal to 3 start absolute value x minus 4 end absolute value plus 1 ?

A
Image with description On a coordinate plane, the scale on the x axis ranges from negative 1 to 9 in increments of 1, and the scale on the y axis ranges from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (4 comma 1) and the graph passes through the points (3 comma 4) and (5 comma 4).
B
Image with description On a Cartesian coordinate system, the x-axis labeled from negative 3 to 7 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (4 comma negative 1). From this point, the curve opens downwards, with its left branch passing through (3 comma negative 4) and (2 comma negative 7), and its right branch passing through (5 comma negative 4) and (6 comma negative 7).
C
Image with description On a Cartesian coordinate system, the x-axis labeled from negative 9 to 1 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma 1). From this point, the curve opens downwards, with its left branch passing through (negative 5 comma negative 2) and (negative 6 comma negative 5), and its right branch passing through (negative 3 comma negative 2) and (negative 2 comma negative 5).
D
Image with description On a Cartesian coordinate system, the x-axis labeled from negative 8 to 2 in increments of 1 and y-axis labeled from negative 3 to 7 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma negative 1). From this point, the curve opens upwards, with its left branch passing through (negative 5 comma 2) and (negative 6 comma 5), and its right branch passing through (negative 3 comma 2) and (negative 2 comma 5).
2
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Fuaad solved an absolute value inequality and expressed the solution as negative 12 is less than x comma x is less than 7 What is another way to show Fuaad’s solution?

A
the union of open paren infinity close paren and open paren 7 close paren
B
start set x such that x is greater than negative 12 or x comma negative 12 or x is less than 7 end set
C
start set x such that negative 12 is less than x comma x is less than 7 end set
D
left parenthesis negative 12 comma 7 right bracket
3

The equation of the piecewise defined function f of x is shown. What is the value of f of negative 2 ? f of x equals enlarged left-brace first row negative x squared comma x less than negative 2. Second row 3 comma negative 2 less than or equal to x less than 0. Third row 3 x plus 2 comma x greater than or equal to 0.

A
f of negative 2 is equal to negative 4
B
f of negative 2 is equal to negative 6
C
f of negative 2 is equal to 3
D
f of negative 2 is equal to 0
4

Which of the following describes the graph of y is equal to lfloor x minus 2 rfloor ?

A
The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .
B
The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 3 for negative 2 is less than x comma x is less than or equal to negative 1 .
C
The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 3 for negative 2 is less than or equal to x comma x is less than negative 1 .
D
The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .
5

If f of x is equal to the fraction with numerator x minus 6 and denominator x , g of x is equal to x plus 4 , and h of x is equal to 3 x minus 2 , what is open paren h circ f circ g close paren times x ?

A
open paren h circ f circ g close paren times x is equal to the fraction with numerator 3 x minus 4 and denominator x
B
open paren h circ f circ g close paren times x is equal to the fraction with numerator x minus 2 and denominator x plus 4
C
open paren h circ f circ g close paren times x is equal to the fraction with numerator 3 x minus 8 and denominator x
D
open paren h circ f circ g close paren times x is equal to the fraction with numerator x minus 14 and denominator x plus 4
6

A customer deposits 1 dollars comma 000 in an account in which the interest is compounded annually. The table shows the balances in the account at the end of each year. Amount in Account vs. Number of Years Amount in Account, cap A Number of Years After Initial Deposit, t 1 comma 000 0 1 comma 080 1 1 comma 166 point 4 0 2 1 comma 259 point 7 1 3 1 comma 360 point 4 9 4 Which equation best represents the data in the table?

A
cap A is equal to 1000 times 1 point 0 8 to the t th power
B
cap A is equal to 1000 times 1 point 8 to the t th power
C
cap A is equal to 800 to the t th power
D
cap A is equal to 1080 to the t th power
7

A customer deposits 500 dollars in an account that pays 4 percent annual interest. What is the balance after 3 years if the interest is compounded annually? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t = years since initial deposit n = number of times compounded per year r = annual interest rate (as a decimal) cap p = initial (principal) investment cap v times t = value of investment after t years

A
512 point 0 0 dollars
B
500 point 1 2 dollars
C
560 point 0 0 dollars
D
562 point 4 3 dollars
8

The quantity n varies jointly with the product of z and the square of the sum of x and y When x is equal to 2 , y is equal to 1 , and z is equal to 3 , n is equal to 18 What is the constant of variation?

A
2 thirds
B
1 ninth
C
2
D
6 fifths
9

Which statement best compares the graphs of f of x is equal to lfloor x rfloor and f of x is equal to lceil x rceil ?

A
The graph of f of x is equal to lceil x rceil is shifted up compared to the graph of f of x is equal to lfloor x rfloor , and the open and closed circles are the same.
B
The two graphs are exactly the same.
C
The graph of f of x is equal to lceil x rceil is shifted up compared to the graph of f of x is equal to lfloor x rfloor , and the open and closed circles are reversed.
D
The open and closed circles are reversed.
10

When m is equal to 2 and p is equal to 1 fourth , j is equal to 32 If j varies directly with m and inversely with p , what is the constant of variation?

A
64
B
256
C
4
D
16
11

Which graph shows the solution to the inequality start absolute value x plus 3 end absolute value is greater than or equal to 2 ?

A
Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on negative 5 and negative 1 and are connected.
B
Image with description Number line extending indefinitely in both directions, indicated by arrows at each end. Solid points are marked at 1 and 5. The highlighted line extends from negative infinity to 1, and from 5 to positive infinity, with both endpoints included. This represents all numbers less than or equal to 1, or greater than or equal to 5.
C
Image with description Number line extending indefinitely in both directions, indicated by arrows at each end. Solid points are marked at negative 5 and negative 1. A highlighted line begins at negative 5, passes through negative 1, and continues infinitely to the left and right. This represents all real numbers on the number line, with negative 5 and negative 1 included.
D
Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on 1 and 5 and are connected.
12

If f of x is equal to e to the x th power and g of x is equal to x minus 4 , what is open paren g circ f close paren times x ?

A
open paren g circ f close paren times x is equal to e to the x th power minus 4
B
open paren g circ f close paren times x is equal to e raised to the x minus 4 power
C
open paren g circ f close paren times x is equal to e raised to the x minus 4 power minus 4
D
open paren g circ f close paren times x is equal to e to the x th power plus x minus 4
13

Which statement is true about f of x plus 2 is equal to 1 sixth start absolute value x minus 3 end absolute value ?

A
The graph of f of x opens downward.
B
The graph of f of x is a horizontal compression of the graph of the parent function.
C
The graph of f of x has a vertex of open paren negative 3 comma 2 close paren .
D
The graph of f of x has range of f of x is greater than or equal to negative 2 .
14

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

A
exponential
B
cube root
C
square root
D
absolute value
15

If she orders 75 shirts and passes the cost along to the employees, what would each employee owe for the shirt if each pays the same amount? Round to the nearest cent.

A
7 point 4 7 dollars
B
7 point 6 6 dollars
C
7 point 4 0 dollars
D
7 point 5 3 dollars
16

What are the domain and range of the function f of x is equal to 5 raised to the x minus 3 power plus 1 ?

A
domain: all real numbers less than 5 range: all real numbers greater than 1
B
domain: all real numbers greater than 1 range: all real numbers
C
domain: all real numbers range: all real numbers greater than 0
D
domain: all real numbers range: all real numbers greater than 1
17

What are the domain and range of the function?

A
domain: open paren negative 2 comma infinity close paren range: open paren negative infinity comma infinity close paren
B
domain: open paren negative infinity comma infinity close paren range: left bracket negative 2 comma infinity right parenthesis
C
domain: open paren negative 3 comma 0 close paren range: left bracket negative 2 comma infinity right parenthesis
D
domain: open paren negative 4 comma 0 close paren range: open paren negative 2 comma infinity close paren
18

The graph is an example of which type of function?

A
square root
B
linear
C
quadratic
D
cubic

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