AnswersAlgebraic ReasoningGraphing Logarithmic Functions

Graphing Logarithmic Functions — Quiz Answers

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1
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Which of the following is the inverse of y is equal to 3 to the x th power ?

A
y is equal to 1 third to the x th power
B
y is equal to the log base 3 of x
C
y is equal to the fraction with numerator 1 and denominator 3 to the x th power
D
y is equal to the log base 1 third of x
2
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What is the domain of y is equal to the log base 5 of x ?

A
all real numbers
B
all real numbers less than 0
C
all real numbers not equal to 0
D
all real numbers greater than 0
3

Which of the following is a logarithmic function?

A
y is equal to the log base 3 of x
B
y is equal to x plus 3
C
y is equal to 3 to the x th power
D
y is equal to x cubed
4

Which statement is true?

A
y is equal to the log base 3 fourths of x is not a logarithmic function because the base is a fraction.
B
y is equal to the log base 10 of x is not a logarithmic function because the base is greater than 0 .
C
y is equal to the log base square root of 3 of x is not a logarithmic function because the base is a square root.
D
y is equal to the log base 1 of x is not a logarithmic function because the base is equal to 1 .
5

What are the domain and range of f of x is equal to log x minus 5 ?

A
domain: x is greater than 5 ; range: y is greater than 5
B
domain: x is greater than 0 ; range: all real numbers
C
domain: x is less than 0 ; range: all real numbers
D
domain: x is greater than 5 ; range: y is greater than negative 5
6

Which of the following is the inverse of y is equal to 6 to the x th power ?

A
y is equal to the log base x of 6
B
y is equal to the log base 1 sixth of x
C
y is equal to the log base 6 of x
D
y is equal to the log base the log base 6 of 6 of x
7

Which of the following is a logarithmic function?

A
y is equal to the log base 0 point 2 5 of x
B
y is equal to 0 point 2 5 x
C
y is equal to x raised to the 0 point 2 5 power
D
y is equal to 0 point 2 5 to the x th power
8

What is the range of y is equal to the log base 8 of x ?

A
all real numbers less than 0
B
all real numbers
C
all real numbers not equal to 0
D
all real numbers greater than 0
9

Which statement is true?

A
The graph of y is equal to log sub b of x plus 4 is the graph of y is equal to log sub b of x translated 4 units up.
B
The graph of y is equal to log sub b of x minus 4 is the graph of y is equal to log sub b of x translated 4 units left.
C
The graph of y is equal to log sub b of open paren x minus 4 close paren is the graph of y is equal to log sub b of x translated 4 units down.
D
The graph of y is equal to log sub b of open paren x plus 4 close paren is the graph of y is equal to log sub b of x translated 4 units right.
10

Which is the graph of y is equal to negative log times open paren x minus 2 close paren plus 3 ?

A
Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 7 to 7 by 1. The graph has a curve that originates from (2 comma negative 4), moves up, intersects the x-axis at (3 comma 0), and goes through (9 comma 2).
B
Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 7 to 7 by 1. The graph has a curve that originates from (2 comma 0), moves up, and goes through (3 comma 3) and (9 comma 5).
C
Image with description On a coordinate plane, the x-axis lists negative 3 to 11 by 1, and the y-axis lists negative 5 to 9 by 1. The graph has a curve that originates from (2 comma 5), goes down, passes through (3 comma 3), and (11 comma 2).
D
Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 7 to 7 by 1. The graph has a curve that starts from (2 comma 4), goes down, intersects the x-axis at (3 comma 0), and goes through (5 comma negative 1) and (9 comma negative 2).
11

Which of the following is a logarithmic function?

A
y is equal to x cubed
B
y is equal to x plus 3
C
y is equal to 3 to the x th power
D
y is equal to the log base 3 of x
12

What is the domain of the function?

A
x is greater than negative 2
B
x is less than 2
C
x is greater than 0
D
all real numbers
13

Which of the following is the inverse of y is equal to 6 to the x th power ?

A
y is equal to the log base 6 of x
B
y is equal to the log base x of 6
C
y is equal to the log base the log base 6 of 6 of x
D
y is equal to the log base 1 sixth of x
14

Which function is shown in the graph?

A
y is equal to the log base 6 of x
B
y is equal to the log base 1 sixth of x
C
y is equal to the log base 0 point 5 of x
D
y is equal to the log base 1 of x
15

Which is the graph of a logarithmic function?

A
Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a hyperbola. The curve above the x-axis has a vertex at (4 comma 1) and the curve below the x-axis has a vertex at (2 comma negative 1).
B
Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a straight line with a negative slope that has an x-intercept at (3 comma 0) and a y-intercept at (0 comma 3).
C
Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a curve that originates from (0 comma negative 2 point 5), moves up, and intersects the x-axis at (1 comma 0). It passes through (3 comma 1) and (8 comma 2).
D
Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a parabola that opens upwards, with a vertex at (4 comma 0). It passes through (2 comma 4) and (6 comma 4).
16

Which table represents the graph of a logarithmic function in the form y is equal to the log base b of x when b is greater than 1 ?

A
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 1 point 9'; Column 2, 'negative 2 point 0 9 6' Row 3: Column 1, 'negative 1 point 7 5'; Column 2, 'negative 1 point 2 6 2' Row 4: Column 1, 'negative 1 point 5'; Column 2, 'negative point 6 3 0 9' Row 5: Column 1, 'negative 1'; Column 2, '0' Row 6: Column 1, '2'; Column 2, 'point 6 3 0 9'
B
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '9 eighths'; Column 2, '3' Row 3: Column 1, '1 point 2 5'; Column 2, '2' Row 4: Column 1, '1 point 5'; Column 2, '1' Row 5: Column 1, '1 point 7 5'; Column 2, 'point 4 1 5' Row 6: Column 1, '2'; Column 2, '0'
C
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1 eighth'; Column 2, '0' Row 3: Column 1, '1 fourth'; Column 2, '1' Row 4: Column 1, '1 half'; Column 2, '2' Row 5: Column 1, '1'; Column 2, '3' Row 6: Column 1, '2'; Column 2, '4'
D
Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1 eighth'; Column 2, 'negative 3' Row 3: Column 1, '1 fourth'; Column 2, 'negative 2' Row 4: Column 1, '1 half'; Column 2, 'negative 1' Row 5: Column 1, '1'; Column 2, '0' Row 6: Column 1, '2'; Column 2, '1'
17

What is the range of y is equal to the log base 8 of x ?

A
all real numbers
B
all real numbers not equal to 0
C
all real numbers greater than 0
D
all real numbers less than 0
18

Which properties are present in a table that represents a logarithmic function in the form y is equal to the log base b of x when b is greater than 1 ? I The y -values are always increasing or always decreasing. II The point open paren 0 comma 1 close paren exists in the table. III The y -values will decrease rapidly as the x -values approach zero. IV There will only be one x -value in the table with a y -value of zero.

A
I, III, and IV
B
I and II only
C
I only
D
II and III only
19

What are the domain and range of f of x is equal to log x minus 5 ?

A
domain: x is less than 0 ; range: all real numbers
B
domain: x is greater than 0 ; range: all real numbers
C
domain: x is greater than 5 ; range: y is greater than negative 5
D
domain: x is greater than 5 ; range: y is greater than 5
20

What is the domain and range of f⁡(x)=10⁢log_7⁡x ? Enter your answers as an inequality. Enter your answers in the boxes.

Answer:

x>0|-∞<y<∞

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