Practice Exam Answers

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Which table identifies the left-hand and right-hand limits at the endpoints?

A
Table with 2 columns and 4 rows.Row 1: Column 1, 'limit x to negative 4 raised to the negative power of f times x'; Column 2, '5' Row 2: Column 1, 'limit x to negative 4 raised to the plus power of f times x'; Column 2, 'DNE' Row 3: Column 1, 'limit x to 2 raised to the negative power of f times x'; Column 2, 'DNE' Row 4: Column 1, 'limit x to 2 raised to the plus power of f times x'; Column 2, '2'
B
Table with 2 columns and 4 rows.Row 1: Column 1, 'limit x to negative 4 raised to the negative power of f times x'; Column 2, 'DNE' Row 2: Column 1, 'limit x to negative 4 raised to the plus power of f times x'; Column 2, '5' Row 3: Column 1, 'limit x to 2 raised to the negative power of f times x'; Column 2, '2' Row 4: Column 1, 'limit x to 2 raised to the plus power of f times x'; Column 2, 'DNE'
C
Table with 2 columns and 4 rows.Row 1: Column 1, 'limit x to negative 4 raised to the negative power of f times x'; Column 2, 'DNE' Row 2: Column 1, 'limit x to negative 4 raised to the plus power of f times x'; Column 2, 'DNE' Row 3: Column 1, 'limit x to 2 raised to the negative power of f times x'; Column 2, '2' Row 4: Column 1, 'limit x to 2 raised to the plus power of f times x'; Column 2, '2'
D
Table with 2 columns and 4 rows.Row 1: Column 1, 'limit x to negative 4 raised to the negative power of f times x'; Column 2, '5' Row 2: Column 1, 'limit x to negative 4 raised to the plus power of f times x'; Column 2, '5' Row 3: Column 1, 'limit x to 2 raised to the negative power of f times x'; Column 2, '2' Row 4: Column 1, 'limit x to 2 raised to the plus power of f times x'; Column 2, '2'
3

Using cap v is equal to l w h , what is an expression for the volume of the following rectangular prism? Expand Image

A
15 over 2 x
B
the fraction with numerator 3 x plus 12 and denominator 2 x plus 8
C
the fraction with numerator 15 and denominator 2 x plus 2
D
15 eighths
8

Function g of x has a removable discontinuity at x is equal to c , where g of c is undefined. Which statement describes the one-sided limits at x is equal to c ?

A
limit x to c raised to the negative power of g x DNE limit x to c raised to the plus power of g times x is equal to b [for some value b ]
B
limit x to c raised to the negative power of g x DNE limit x to c raised to the plus power of g x DNE
C
limit x to c raised to the negative power of g times x is equal to A limit x to c raised to the plus power of g times x is equal to A [for some value A ]
D
limit x to c raised to the negative power of g times x is equal to A limit x to c raised to the plus power of g times x is equal to b [for distinct value A and b ]
10

What is the general equation of a sine function with an amplitude of 6 , a period of pi over 4 , and a horizontal shift of pi over 2 ?

A
y is equal to 8 sine open paren 4 times open paren x minus pi over 2 close paren close paren
B
y is equal to 6 sine open paren 8 times open paren x minus pi over 2 close paren close paren
C
y is equal to 6 sine 8 x plus pi over 2
D
y is equal to sine of open paren 8 times open paren x minus pi over 2 close paren close paren
11

If f of negative 5 is equal to 0 , what are all the factors of the function f of x is equal to x cubed minus 19 x plus 30 ? Use the Remainder Theorem.

A
open paren x plus 2 close paren times open paren x minus 5 close paren times open paren x plus 3 close paren
B
open paren x minus 2 close paren times open paren x plus 5 close paren times open paren x minus 3 close paren
C
open paren x plus 2 close paren times open paren x minus 5 close paren
D
open paren x minus 2 close paren times open paren x plus 5 close paren
12

The parent cosecant function is shifted 2 units down, and its period is changed to 6 pi Which of the following is the graph of the transformed function?

A
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (3 by 2 pi comma1) and (negative 9 by 2 pi comma 1). Another line y equals negative 1 touches at (9 by 2 pi comma negative 1) and (negative 3 by 2 pi comma negative 1).
B
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 2 touches at (3 pi comma negative 1) and (negative 3 pi comma negative 1).
C
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 3 touches at (3 pi comma negative 3) and (negative 3 pi comma negative 3).
D
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 1 at (3 by 2 pi comma negative 1) and (negative 9 by 2 pi comma negative 1). Another line y equals negative 3 touches at (3 by 2 pi comma negative 3) and (negative 9 by 2 pi comma negative 3).
14

On interval 0 is less than or equal to x comma x is less than 2 pi , where are the x -intercepts of y is equal to cosine of 2 x ?

A
pi over 2 and the fraction with numerator 3 mathrm pi and denominator 2
B
pi over 4 , 3 pi over 4 , 5 pi over 4 , and the fraction with numerator 7 mathrm pi and denominator 4
C
pi over 2 , pi , and the fraction with numerator 3 mathrm pi and denominator 2
D
0 , pi , and 2 pi
15

What is the general equation of a sine function with an amplitude of 6 , a period of pi over 4 , and a horizontal shift of pi over 2 ?

A
y is equal to sine of open paren 8 times open paren x minus pi over 2 close paren close paren
B
y is equal to 6 sine open paren 8 times open paren x minus pi over 2 close paren close paren
C
y is equal to 6 sine 8 x plus pi over 2
D
y is equal to 8 sine open paren 4 times open paren x minus pi over 2 close paren close paren
16

For function f of x , which condition implies a horizontal asymptote at y is equal to 31 ?

A
limit x to infinity of f times x is equal to 31
B
limit x to 31 raised to the plus power of f times x is equal to infinity and limit x to 31 raised to the negative power of f times x is equal to negative infinity
C
limit x to c raised to the plus power of f times x is equal to 31 and limit x to c raised to the negative power of f times x is equal to 31 for some value of c
D
limit x to 31 of f times x is equal to infinity
18

Which is the simplified form of open paren the fraction with numerator 2 A b and denominator A to the negative 5 power b squared close paren to the negative 3 power ? Assume A is not equal to 0 , b is not equal to 0

A
the fraction with numerator 2 A to the 6th power and denominator b to the 5th power
B
the fraction with numerator b squared and denominator 8 A to the 45th power
C
the fraction with numerator b cubed and denominator 8 A to the 18th power
D
the fraction with numerator A to the 6th power and denominator 4 b
20

On which interval are both the sine and cosine functions increasing?

A
open paren 0 comma pi close paren
B
open paren 3 pi over 2 comma 2 pi close paren
C
open paren pi over 2 comma pi close paren
D
open paren pi comma 3 pi over 2 close paren

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