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The tables show two functions evaluated for the given values of x x negative 8 negative 4 4 8 f of x negative 6 negative 2 6 10 x negative 8 negative 4 4 8 g of x 54 10 18 70 Which table shows the values of the combined function determined by dividing g of x by f of x ?

A
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, '1 ninth' Row 3: Column 1, 'negative 4'; Column 2, '1 fifth' Row 4: Column 1, '4'; Column 2, 'negative 1 third' Row 5: Column 1, '8'; Column 2, 'negative 1 seventh'
B
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, 'negative 9' Row 3: Column 1, 'negative 4'; Column 2, 'negative 5' Row 4: Column 1, '4'; Column 2, '3' Row 5: Column 1, '8'; Column 2, '7'
C
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, 'negative 1 ninth' Row 3: Column 1, 'negative 4'; Column 2, 'negative 1 fifth' Row 4: Column 1, '4'; Column 2, '1 third' Row 5: Column 1, '8'; Column 2, '1 seventh'
D
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, '9' Row 3: Column 1, 'negative 4'; Column 2, '5' Row 4: Column 1, '4'; Column 2, 'negative 3' Row 5: Column 1, '8'; Column 2, 'negative 7'
23

If f of x is equal to x squared minus 1 and g of x is equal to 2 x minus 3 , what is the domain of open paren f circ g close paren times x ?

A
open paren negative infinity comma infinity close paren
B
left bracket negative 5 comma infinity right parenthesis
C
open paren infinity comma negative infinity close paren
D
left bracket negative 1 comma infinity right parenthesis
24

The height y , in feet, of a football x seconds after it is thrown is modeled by the equation y is equal to negative 16 x squared plus 24 x plus 1 What information does the zero of the equation 6 is equal to negative 16 x squared plus 24 x plus 1 represent?

A
the horizontal distance traveled by the ball when it is 6 ft above the ground
B
the initial upward velocity of the ball
C
when the ball is 6 ft above the ground
D
the height of the ball after 6 seconds
25

Which function is a quadratic function?

A
q times x is equal to open paren 2 x plus 4 close paren cubed plus 3
B
t times x is equal to open paren x minus 4 close paren squared plus 3
C
r times x is equal to open paren negative 6 x minus 4 close paren to the 4th power plus 3 times open paren x plus 2 close paren squared
D
s times x is equal to negative open paren x minus 6 close paren plus 3 times open paren x plus 1 close paren
27

The function h of x is given. h of x is equal to open paren 3 comma negative 5 close paren comma open paren 5 comma negative 7 close paren comma open paren 6 comma negative 9 close paren comma open paren 10 comma negative 12 close paren comma open paren 12 comma negative 16 close paren Which of the following gives h inverse of x ?

A
start set open paren negative 5 comma 3 close paren comma open paren negative 7 comma 5 close paren comma open paren negative 9 comma 6 close paren comma open paren negative 12 comma 10 close paren comma open paren negative 16 comma 12 close paren end set
B
start set open paren 3 comma 5 close paren comma open paren 5 comma 7 close paren comma open paren 6 comma 9 close paren comma open paren 10 comma 12 close paren comma open paren 12 comma 16 close paren end set
C
start set open paren 5 comma 3 close paren comma open paren 7 comma 5 close paren comma open paren 9 comma 6 close paren comma open paren 12 comma 10 close paren comma open paren 16 comma 12 close paren end set
D
start set open paren 3 comma negative 5 close paren comma open paren 5 comma negative 7 close paren comma open paren 6 comma negative 9 close paren comma open paren 10 comma negative 12 close paren comma open paren 12 comma negative 16 close paren end set
28

The minimum of the graph of a quadratic function is located at negative 1 comma 2 The point 2 comma 20 is also on the parabola. Which function represents the situation?

A
f of x is equal to 2 times open paren x plus 1 close paren squared plus 2
B
f of x is equal to open paren x minus 1 close paren squared plus 2
C
f of x is equal to open paren x plus 1 close paren squared plus 2
D
f of x is equal to 2 times open paren x minus 1 close paren squared plus 2
29

Use the zero product property to find the solutions to the equation x squared minus 15 x minus 100 is equal to 0

A
x is equal to 5 or x is equal to 20
B
x is equal to negative 20 or x is equal to negative 5
C
x is equal to negative 20 or x is equal to 5
D
x is equal to negative 5 or x is equal to 20
31

If f of x is a linear function, which statement must be true?

A
f of x has no constant term.
B
f of x has no terms with a coefficient other than 1 .
C
f of x has no x squared -term.
D
f of x has no x -term.
32

The function f of x is equal to 0 point 5 x plus 3 is used to estimate the number of pounds of potatoes a caterer plans to make depending on the number of people being served, x The mathematical domain for the function is the set of real numbers. Which statement describes the limitation for the reasonable domain compared to the mathematical domain?

A
The reasonable domain contains only positive whole numbers.
B
The reasonable domain contains only positive real numbers.
C
The reasonable domain contains only real numbers greater than 3 .
D
The reasonable domain contains only rational numbers greater than 3 .
33

What is the equation of the line parallel to 3 x plus 5 y is equal to 11 that passes through the point open paren 15 comma 4 close paren ?

A
y is equal to negative 3 fifths x plus 5
B
y is equal to 5 thirds x minus 29
C
y is equal to 5 thirds x minus 21
D
y is equal to negative 3 fifths x plus 13
34

If three times a number is at least four more than eight times the number, which of the following is true?

A
The number is at least four-fifths.
B
The number is at least negative four-fifths.
C
The number is at most four-fifths.
D
The number is at most negative four-fifths.
35

For which pair of functions is open paren g circ f close paren times A is equal to absolute value of A minus 2 ?

A
f of A is equal to 5 plus A squared and g of A is equal to square root of A minus 5 end root minus 2
B
f of A is equal to 1 half A minus 1 and g of A is equal to 2 A minus 2
C
f of A is equal to A squared minus 4 and g of A is equal to square root of A
D
f of A is equal to 3 minus 3 A and g of A is equal to 4 A minus 5
36

Which expression is equivalent to open paren f plus g close paren of 4 ?

A
f of open paren 4 plus g of 4 close paren
B
4 times open paren f of x plus g of x close paren
C
f of x plus g of 4
D
f of 4 plus g of 4
37

Which table shows a linear function?

A
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '0'; Column 2, 'negative 2' Row 3: Column 1, '1'; Column 2, '0' Row 4: Column 1, '2'; Column 2, '2' Row 5: Column 1, '3'; Column 2, '7' Row 6: Column 1, '4'; Column 2, '14'
B
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 6'; Column 2, 'negative 16' Row 3: Column 1, 'negative 2'; Column 2, 'negative 8' Row 4: Column 1, '0'; Column 2, 'negative 4' Row 5: Column 1, '1'; Column 2, 'negative 2' Row 6: Column 1, '3'; Column 2, '2'
C
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 4'; Column 2, '8' Row 3: Column 1, 'negative 1'; Column 2, '2' Row 4: Column 1, '1'; Column 2, '2' Row 5: Column 1, '2'; Column 2, '4' Row 6: Column 1, '3'; Column 2, '6'
D
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 2'; Column 2, 'negative 7' Row 3: Column 1, 'negative 1'; Column 2, '0' Row 4: Column 1, '0'; Column 2, '1' Row 5: Column 1, '1'; Column 2, '2' Row 6: Column 1, '2'; Column 2, '9'
39

What is the inverse of the function f of x is equal to 4 x plus 8 ?

A
h of x is equal to 1 half x plus 2
B
h of x is equal to 1 fourth x plus 2
C
h of x is equal to 1 half x minus 2
D
h of x is equal to 1 fourth x minus 2
41

If g of x is the inverse of f of x and f of x is equal to 4 x plus 12 , what is g of x ?

A
g of x is equal to 1 fourth x minus 3
B
g of x is equal to x minus 3
C
g of x is equal to 1 fourth x minus 12
D
g of x is equal to 12 x plus 4

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N/A — Exam Answers — Algebraic Reasoning