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Use synthetic division to solve open paren x cubed minus x squared minus 17 x minus 15 close paren divided by open paren x minus 5 close paren What is the quotient?

A
x squared plus 4 x plus 3
B
x squared minus 6 x plus 13 minus the fraction with numerator 80 and denominator x plus 5
C
x squared minus 6 x plus 13 minus the fraction with numerator 80 and denominator x minus 5
D
x cubed plus 4 x squared plus 3 x
23

For function f of x , which pair of limits would verify the existence of a vertical asymptote at x is equal to negative 1 ?

A
limit x to negative infinity of f times x is equal to negative 1 and limit x to infinity of f times x is equal to negative 1
B
limit x to c raised to the negative power of f times x is equal to negative 1 and limit x to c raised to the plus power of f times x is equal to negative 1 for some value c
C
limit x to negative 1 raised to the negative power of f times x is equal to c and limit x to negative 1 raised to the plus power of f times x is equal to c for some value c
D
limit x to negative 1 raised to the negative power of f times x is equal to infinity and limit x to negative 1 raised to the plus power of f times x is equal to infinity
24

What is the solution of the fraction with numerator 1 and denominator c minus 3 minus 1 over c is equal to the fraction with numerator 3 and denominator c times open paren c minus 3 close paren ?

A
c is equal to 0 and c is equal to 3
B
all real numbers
C
all real numbers, except c is not equal to 0 and c is not equal to 3
D
no solution
25

What is the quotient and remainder, written as partial fractions, of the fraction with numerator 4 x cubed plus 11 x squared minus 9 and denominator x squared plus 3 x plus 2 ?

A
4 x minus 1 minus the fraction with numerator 2 and denominator x plus 1 plus the fraction with numerator 3 and denominator x plus 2
B
4 x minus 1 plus the fraction with numerator 2 and denominator x plus 1 minus the fraction with numerator 7 and denominator x plus 2
C
4 x minus 1 minus the fraction with numerator 2 and denominator x plus 1 minus the fraction with numerator 3 and denominator x plus 2
D
4 x minus 1 plus the fraction with numerator 2 and denominator x plus 1 plus the fraction with numerator 7 and denominator x plus 2
28

Which trigonometric functions have a domain of left bracket negative 1 comma 1 right bracket ?

A
y is equal to arcsin x and y is equal to arctan x
B
y is equal to arcsin x and y is equal to arccos x
C
y is equal to arccos x and y is equal to arctan x
D
y is equal to operatorname ar cs e c x and y is equal to operatorname ar c cs c x
29

At which x -value does the cosine function attain a maximum value?

A
x is equal to 1
B
x is equal to 0
C
x is equal to pi over 2
D
x=3⁢π2
30

Which statement correctly identifies an asymptote of g of x is equal to the fraction with numerator 42 x cubed minus 15 and denominator 7 x cubed minus 4 x squared minus 3 using limits?

A
limit x to plus or minus infinity of g times x is equal to 6 , so g of x has an asymptote at y is equal to 6 .
B
limit x to plus or minus infinity of g times x is equal to 6 , so g of x has an asymptote at x is equal to 6 .
C
limit x to plus or minus infinity of g times x is equal to 5 , so g of x has an asymptote at y is equal to 5 .
D
limit x to plus or minus infinity of g times x is equal to 5 , so g of x has an asymptote at x is equal to 5 .
31

Which equation describes a rational function with x -intercepts at negative 4 and 2 , a vertical asymptote at x is equal to 1 and x is equal to negative 1 , and a horizontal asymptote at y is equal to negative 3 ?

A
f of x is equal to the fraction with numerator x squared minus 1 and denominator negative 3 open paren x minus 4 close paren open paren x plus 2 close paren
B
f of x is equal to the fraction with numerator negative 3 open paren x minus 4 close paren open paren x plus 2 close paren and denominator x squared minus 1
C
f of x is equal to the fraction with numerator negative 3 open paren x plus 4 close paren open paren x minus 2 close paren and denominator x squared minus 1
D
f of x is equal to the fraction with numerator x squared minus 1 and denominator negative 3 open paren x plus 4 close paren open paren x minus 2 close paren
33

Consider the function f of x is equal to 6 sine open paren x minus pi over 8 close paren plus 8 What transformation results in g of x is equal to 6 sine open paren x minus 7 pi over 16 close paren plus 1 ?

A
Translate 5 pi over 16 units left and 7 units up.
B
Translate 5 pi over 16 units left and 7 units down.
C
Translate 5 pi over 16 units right and 7 units down.
D
Translate 5 pi over 16 units right and 7 units up.
34

If the function y is equal to sine of x is transformed to y is equal to sine of 2 x , how does the graph change?

A
It is stretched vertically.
B
It is stretched horizontally.
C
It is compressed horizontally.
D
It is compressed vertically.
36

Which expression is equivalent to cosine 120 degrees ?

A
cosine 420 degrees
B
cosine 60 degrees
C
cosine 300 degrees
D
cosine 240 degrees
37

Which expression is equivalent to the fraction with numerator 10 x to the 6th power y to the 12th power and denominator negative 5 x to the negative 2 power y to the negative 6 power ? Assume x is not equal to 0 , y is not equal to 0

A
negative 50 x to the 8th power y to the 18th power
B
negative 2 x to the 8th power y to the 18th power
C
negative 2 x to the 12th power y to the 72th power
D
5 x to the 8th power y to the 18th power
38

Which expression is equivalent to the fraction with numerator 4 A plus 4 and denominator 2 A times the fraction with numerator A squared and denominator A plus 1 ?

A
2 A
B
the fraction with numerator 6 A squared and denominator A plus 1
C
6 A
D
the fraction with numerator 2 times open paren A plus 1 close paren squared and denominator A cubed
39

What are the domain and range of f of x is equal to start absolute value x plus 6 end absolute value ?

A
domain: x is less than or equal to negative 6 ; range: open paren negative infinity comma infinity close paren
B
domain: open paren negative infinity comma infinity close paren ; range: f of x is greater than or equal to 0
C
domain: open paren negative infinity comma infinity close paren ; range: f of x is less than or equal to 0
D
domain: x is greater than or equal to negative 6 ; range: open paren negative infinity comma infinity close paren
40

According to the Rational Root Theorem, negative 2 fifths is a potential rational root of which function?

A
f of x is equal to 4 x to the 4th power minus 7 x squared plus x plus 25
B
f of x is equal to 25 x to the 4th power minus 7 x squared plus x plus 4
C
f of x is equal to 10 x to the 4th power minus 7 x squared plus x plus 9
D
f of x is equal to 9 x to the 4th power minus 7 x squared plus x plus 10

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N/A — Exam Answers — Precalculus