AnswersPrecalculusModeling with Rational and Piecewise-Defined Functions: Part Two

Modeling with Rational and Piecewise-Defined Functions: Part Two — Test Answers

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Which two discontinuities does the graph show?

A
endpoint discontinuity at x is equal to negative 2 ; mixed discontinuity at x is equal to 0
B
endpoint discontinuity at x is equal to negative 2 ; infinite discontinuity at x is equal to 0
C
jump discontinuity at x is equal to negative 2 ; infinite discontinuity at x is equal to 0
D
jump discontinuity at x is equal to negative 2 ; mixed discontinuity at x is equal to 0
2
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If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

A
11
B
10
C
12
D
5
3

What is the limit? limit x to negative 19 raised to the plus power of k times x

A
43 point 5
B
44
C
37 point 5
D
38
4

The function shown has an endpoint discontinuity. Which statement describes the one-sided limits at the discontinuity?

A
limit x to 1 raised to the negative power of f x DNE limit x to 1 raised to the plus power of f x DNE
B
limit x to 1 raised to the negative power of f times x is equal to 2 limit x to 1 raised to the plus power of f x DNE
C
limit x to 1 raised to the negative power of f times x is equal to negative 2 limit x to 1 raised to the plus power of f x cap d cap n cap e
D
limit x to 1 raised to the negative power of f x cap d cap n cap e limit x to 1 raised to the plus power of f times x is equal to negative 2
5

The equation of the piecewise defined function f of x is shown. What is the value of f of 1 ? f of x equals enlarged left-brace first row x squared plus 1 comma negative 4 less than or equal to x less than 1. Second row negative x squared comma 1 less than or equal to x less than 2. Third row 3 x comma x greater than or equal to 2.

A
f of 1 is equal to 3
B
f of 1 is equal to 2
C
f of 1 is equal to negative 1
D
f of 1 is equal to negative 2
6

Given f of x is equal to 3 and g x is equal to cosine of x What is the limit? limit x to negative pi of open bracket f of x minus g of x close bracket

A
4
B
DNE
C
3
D
2
7

Given f of x equals inequality 2 cosine pi x comma for x is less than or equal to negative 1 inequality 2 over cosine pi x comma for x is greater than negative 1 What is the limit? limit x to negative 1 of f times x

A
1
B
2
C
negative 1
D
negative 2
8

Over the closed interval left bracket 3 comma 8 right bracket , for which function can the extreme value theorem be applied?

A
h of x is equal to the fraction with numerator open paren x minus 5 close paren times open paren x minus 1 close paren and denominator x squared minus 25
B
h of x equals inequality negative x comma x is less than 5 inequality x squared minus 20 comma x is greater than or equal to 5
C
h of x equals inequality the fraction with numerator 9 x and denominator 10 minus x comma x is less than 4 inequality x plus 2 comma x is greater than or equal to 4
D
h of x is equal to the fraction with numerator negative 2 and denominator 5 times open paren x minus 4 close paren squared
9

What is the horizontal asymptote of j times x is equal to the fraction with numerator 14 x cubed plus 45 and denominator 2 x cubed plus x plus 9 ?

A
y is equal to 5
B
y is equal to 1
C
y is equal to 7
D
y is equal to 12
10

Which piecewise relation defines a function?

A
y equals enlarged left-brace first row x squared comma x less than negative 2. Second row 0 comma negative 2 less than or equal to x less than or equal to 4. Third row negative x squared comma x greater than or equal to 4.
B
y equals enlarged left-brace first row negative 3 x comma x less than negative 2. Second row 3 comma 0 less than or equal to x less than 4. Third row 2 x comma x greater than or equal to 4.
C
y equals enlarged left-brace first row x squared comma x less than or equal to negative 2. Second row 4 comma negative 2 less than x less than or equal to 2. Third row x squared plus 1 comma x greater than or equal to 2.
D
y equals enlarged left-brace first row negative 3 x comma x less than negative 4. Second row 3 comma negative 5 less than x less than 1. Third row 2 x comma x greater than or equal to 1.
11

Which function is continuous at x is equal to 18 ?

A
f of x is equal to the fraction with numerator open paren x minus 18 close paren squared and denominator x
B
f of x is equal to tangent of open paren pi over 36 x close paren
C
f of x is equal to the fraction with numerator x squared minus 17 x minus 18 and denominator x minus 18
D
f of x inequality x squared comma x is not equal to 18 inequality 36 comma comma x equals 18
12

If f of x is equal to 3 lfloor x minus 2 rfloor , what is f of 5 point 9 ?

A
10
B
12
C
9
D
11
13

The standard diameter of a golf ball is 42 point 6 7 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0 point 0 0 2 mm. Which function could represent this situation?

A
f of x is equal to absolute value of x minus 42 point 6 7
B
f of x is equal to x minus absolute value of 42 point 6 7
C
f of x is equal to 42 point 6 7 minus absolute value of x
D
f of x is equal to start absolute value 42 point 6 7 minus x end absolute value
14

In a certain country, a letter up to 1 ounce requires postage in the amount of 0 point 4 2 dollars , and each additional ounce (or fraction of an ounce) has an additional cost. The function represents the cost of mailing one letter with a weight of x ounces in this country. f of x is equal to 0 point 4 2 plus 0 point 2 0 lceil x minus 1 rceil Josiah has two letters. The first weighs 2 point 9 ounces, and the second weighs 4 point 1 ounces. What is the total amount Josiah can expect to pay for postage?

A
2 point 0 4 dollars
B
1 point 8 4 dollars
C
1 point 6 4 dollars
D
1 point 6 2 dollars
15

A company manufactures 16 -oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0 point 1 5 oz, the production is stopped. What is the range of acceptable values for production to continue?

A
16 point 1 5 oz to 16 point 4 5 oz
B
15 point 1 5 oz to 16 point 0 0 oz
C
15 point 8 5 oz to 16 point 0 0 oz
D
15 point 8 5 oz to 16 point 1 5 oz
16

What is the limit? limit x to 1 of the fraction with numerator x cubed minus 1 and denominator x minus 1

A
0
B
3
C
1
D
DNE
17

Which statement is true about f of x is equal to negative 2 thirds start absolute value x plus 4 end absolute value minus 6 ?

A
The graph of f of x opens upward.
B
The graph of f of x is a horizontal stretch of the graph of the parent function.
C
The graph of f of x has a vertex of open paren negative 4 comma 6 close paren .
D
The graph of f of x has a domain of x is less than or equal to negative 6 .
18

Which statement correctly uses limits to determine a vertical asymptote of g of x is equal to the fraction with numerator negative 7 open paren x minus 5 close paren squared open paren x plus 6 close paren and denominator open paren x minus 5 close paren times open paren x plus 5 close paren ?

A
There is a vertical asymptote at x is equal to 5 , because limit x to 5 raised to the negative power of g times x is equal to infinity and limit x to 5 raised to the plus power of g times x is equal to negative infinity .
B
There is a vertical asymptote at x is equal to negative 5 , because limit x to negative 5 raised to the negative power of g times x is equal to infinity and limit x to negative 5 raised to the plus power of g times x is equal to negative infinity .
C
There is a vertical asymptote at x is equal to negative 5 , because limit x to negative 5 raised to the negative power of g times x is equal to negative infinity and limit x to negative 5 raised to the plus power of g times x is equal to infinity .
D
There is a vertical asymptote at x is equal to 5 , because limit x to 5 raised to the negative power of g times x is equal to negative infinity and limit x to 5 raised to the plus power of g times x is equal to infinity .
19

What are the domain and range of the step function?

A
domain = {all integers}, range = {all real numbers}
B
domain = {all real numbers}, range = {all real numbers}
C
domain is equal to dot dot dot minus 5 comma negative 2 comma 1 comma 4 comma dot dot dot , range is equal to dot dot dot minus 4 comma negative 1 comma 2 comma 5 comma dot dot dot
D
domain = {all real numbers}, range is equal to dot dot dot minus 4 comma negative 1 comma 2 comma 5 comma dot dot dot
20

What is the limit? limit x to 3 of j times x

A
4
B
3
C
6
D
5

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