Practice Exam Answers

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1
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Which expression is equivalent to open paren x raised to the 1 half power y raised to the negative 1 fourth power z close paren to the negative 2 power ?

A
the fraction with numerator x raised to the 1 half power and denominator y z squared
B
the fraction with numerator x raised to the 1 half power and denominator y raised to the 1 fourth power z squared
C
the fraction with numerator y raised to the 1 half power and denominator x z squared
D
the fraction with numerator x z squared and denominator y raised to the 1 half power
2
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If you are given the graph of g of x is equal to the log base 2 of x , how could you graph f of x is equal to the log base 2 of x plus 5 ?

A
Translate each point of the graph of g x 5 units right.
B
Translate each point of the graph of g x 5 units up.
C
Translate each point of the graph of g x 5 units down.
D
Translate each point of the graph of g x 5 units left.
4

What is the correct order of operations for simplifying the expression the fraction with numerator open paren x plus 3 close paren squared minus open paren x squared plus 9 close paren and denominator 2 x squared ?

A
divide, square the binomial open paren x plus 3 close paren , distribute the negative to the binomial open paren x squared plus 9 close paren , and then simplify the dividend
B
square the binomial open paren x plus 3 close paren , divide, distribute the negative to the binomial open paren x squared plus 9 close paren , and then simplify the dividend
C
square the binomial open paren x plus 3 close paren , distribute the negative to the binomial open paren x squared plus 9 close paren , simplify the dividend, and then divide
D
square the binomial open paren x plus 3 close paren , distribute the negative to the binomial open paren x squared plus 9 close paren , divide, and then simplify the dividend
5

A polynomial function has a root of negative 6 with multiplicity 3 and a root of 2 with multiplicity 4 If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

A
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 1, passing through (5 comma 8), touches x axis at (2 comma 0), curves up and passes through y axis at (0 comma 2). It then moves up and curves down at (negative 3 point 5 comma 6), passes through x axis at (negative 6 comma 0) and moves to quadrant 3 passing through (negative 7 comma negative 8).
B
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 2, passes through (negative 8 comma 8), crosses the x axis at (negative 6 comma 0), moves down and curves up at (negative 3 point 5 comma negative 3), and crosses the y axis at (0 comma negative 1). It then touches the x axis at (2 comma 0) and moves to quadrant 4 passing through (6 comma negative 8).
C
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn.It starts from quadrant 3 passing through (negative 8 comma negative 1 point 5), it touches x axis at (negative 6 comma 0) and moves down and curves up at (negative 0 point 5 comma negative 3). It then passes through x axis at (2 comma 0) and moves to quadrant 1 passing through (4 comma 8).
D
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. it starts from quadrant 2 passing through (negative 8 comma 0 point 9), touches the x axis at (negative 6 comma 0), it curves up and passes through y axis at (0 comma 1 point 5). It then crosses x axis at (2 comma 0) moves to quadrant 4 through (5 comma negative 8).
8

Which of the following shows the graph of y is equal to negative 2 to the x th power minus 1 ?

A
Image with description On a coordinate plane, the curve approaches x axis for negative values of x in the third quadrant. It passes through (negative 1 comma negative 1), (0 comma negative 2), (1 comma negative 4), and decreases rapidly in the fourth quadrant.
B
Image with description On a coordinate plane, the curve approaches x axis for negative values of x in the third quadrant. It passes through (1 comma negative 1), (2, comma negative 2), (3 comma negative 4), and decreases rapidly in the fourth quadrant.
C
Image with description On a coordinate plane, the curve approaches the line y equals 1 for negative values of x in the second quadrant. It passes through the origin, (1 comma negative 1), (2 comma negative 3), and decreases rapidly in the fourth quadrant.
D
Image with description On a coordinate plane, the curve approaches the line y equals negative 1 for negative values of x in the third quadrant. It passes through (0 comma negative 2), (1 comma negative 3), (2 comma negative 5), and decreases rapidly in the fourth quadrant.
9

Which equation has x is equal to 4 as the solution?

A
the log base x of 64 is equal to 4
B
log sub 4 of open paren 3 x plus 4 close paren is equal to 2
C
log sub 3 of open paren 2 x minus 5 close paren is equal to 2
D
the log base x of 16 is equal to 4
10

Which expression is equivalent to the fraction with numerator open paren A squared b to the 4th power c close paren squared times open paren 6 A cubed b close paren times open paren 2 c to the 5th power close paren cubed and denominator 4 A to the 6th power b to the 12th power c cubed ?

A
the fraction with numerator 9 A c to the 14th power and denominator b cubed
B
the fraction with numerator 9 A c to the 7th power and denominator b to the 5th power
C
the fraction with numerator 3 A c to the 7th power and denominator b to the 5th power
D
the fraction with numerator 12 A c to the 14th power and denominator b cubed
11

Which of the following shows the extraneous solution to the logarithmic equation 2 log sub 5 open paren x plus 1 close paren is equal to 2 ?

A
x is equal to negative 4
B
x is equal to negative 6
C
x is equal to negative 2
D
x is equal to negative 1
12

One root of a third degree polynomial function f of x is negative 5 plus 2 i Which statement describes the number and nature of all roots for this function?

A
f of x has two imaginary roots and one real root.
B
f of x has three imaginary roots.
C
f of x has three real roots.
D
f of x has two real roots and one imaginary root.
14

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
C
open paren x minus 2 close paren times open paren x plus 5 close paren times open paren x minus 3 close paren
D
open paren x plus 2 close paren times open paren x minus 5 close paren
15

Which second degree polynomial function has a leading coefficient of 2 and roots negative 3 and 5 ?

A
f of x is equal to 2 x squared minus 4 x minus 30
B
f of x is equal to 2 x squared plus 2 x minus 15
C
f of x is equal to 2 x squared minus 2 x minus 15
D
f of x is equal to 2 x squared plus 4 x minus 30
19

Holly finds that open paren 11 m minus 13 n plus 6 m n close paren minus open paren 10 m minus 7 n plus 3 m n close paren is equal to m minus 20 n plus 9 m n What error did Holly make?

A
She did not combine all like terms.
B
She only used the additive inverses of negative 7 n and 3 m n when combining like terms.
C
She added the polynomials instead of subtracting.
D
She only used the additive inverse of 10 m when combining like terms.
20

The domain of u times x is the set of all real values except 0 and the domain of v times x is the set of all real values except 2 What are the restrictions on the domain of open paren u circ v close paren times x ?

A
x is not equal to 2 and x cannot be any value for which v times x is equal to 0
B
u times x is not equal to 0 and v times x is not equal to 2
C
x is not equal to 0 and x cannot be any value for which u times x is equal to 2
D
u times x is not equal to 2 and v times x is not equal to 0

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