AnswersAlgebra 2 with ProbabilityExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

25 verified answers
1
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Which function is shown in the graph?

A
y is equal to 2 raised to the x minus 3 power plus 2
B
y is equal to 2 raised to the x plus 3 power plus 2
C
y is equal to 2 raised to the x minus 2 power plus 3
D
y is equal to 2 raised to the x plus 2 power plus 3
2
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Which function is graphed?

A
y is equal to 1 third times 3 to the x th power
B
y is equal to 2 to the x th power minus 1
C
y is equal to 1 half to the x th power plus 2
D
y is equal to 3 times 1 third to the x th power
3

What is the domain of the graph of y=6⁢(8)^x−2+5 ? Enter your answer in interval notation. Enter your answers in the boxes.

Answer:

(-∞,∞)

4

Which of the following shows the graph of y is equal to 4 to the x th power plus 3 ?

A
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. It passes through the points (3 comma 1) and (4 comma 4). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.
B
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. The curve passes through the points (negative 3 comma 1), (negative 2 comma 4), and (negative 1 point 5 comma, 8). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.
C
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 3 as x approaches negative infinity. It passes through the points (negative 2 comma 3), (0 comma 4) and (1 comma 7). As x increases, the curve rises sharply towards positive infinity. As x decreases, the curve flattens out, approaching the asymptote at y equals 3.
D
Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals negative 3 as x approaches negative infinity, indicated by an arrow pointing left along the line y equals negative 3. It passes through the y-intercept (0 comma negative 2). The curve goes through the points (negative 1 comma negative 3), (1 comma 1) and (1 point 5 comma 6). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.
5

Which of the following describes the transformations of g of x is equal to negative 2 raised to the x plus 4 power minus 2 from the parent function f of x is equal to 2 to the x th power ?

A
shift 4 units right, reflect over the x -axis, shift 2 units down
B
shift 4 units right, reflect over the y -axis, shift 2 units down
C
shift 4 units left, reflect over the y -axis, shift 2 units down
D
shift 4 units left, reflect over the x -axis, shift 2 units down
6

Which function has a range of y is less than 3 ?

A
y is equal to 3 times 2 to the x th power
B
y is equal to negative 2 to the x th power plus 3
C
y is equal to 2 to the x th power minus 3
D
y is equal to 2 times 3 to the x th power
7

Which function represents a vertical stretch of an exponential function?

A
f of x is equal to 3 times 1 half to the x th power
B
f of x is equal to 3 raised to the 2 x power
C
f of x is equal to 3 raised to the open paren 1 half x close paren power
D
f of x is equal to 1 half times 3 to the x th power
8

Which set of ordered pairs could be generated by an exponential function?

A
open paren 0 comma 1 close paren , open paren 1 comma 3 close paren , open paren 2 comma 9 close paren , open paren 3 comma 27 close paren
B
open paren 0 comma 0 close paren , open paren 1 comma 1 close paren , open paren 2 comma 8 close paren , open paren 3 comma 27 close paren
C
open paren 0 comma 1 close paren , open paren 1 comma 2 close paren , open paren 2 comma 5 close paren , open paren 3 comma 10 close paren
D
open paren 0 comma 0 close paren , open paren 1 comma 3 close paren , open paren 2 comma 6 close paren , open paren 3 comma 9 close paren
9

Which graph represents an exponential function?

A
Image with description On a coordinate plane, the graph is made up of two different curves that do not meet. The x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. The upper left curve is located entirely within the second quadrant. It extends from the far left, approaching the horizontal line y = 2 from above, and rises steeply upwards as it approaches the vertical line x = negative 2 from the left. It passes through (negative 3 comma 3). The lower right curve starts in the third quadrant, approaching the vertical line x = negative 2 from the right. It passes through the point (negative 1 comma 1) and then extends into the first quadrant, approaching the horizontal line y = 2 from below.
B
Image with description On a coordinate plane, the curve is symmetric about y axis in the third and the fourth quadrant. The x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. A parabola opens downwards with its vertex at the origin (0 comma 0). The parabola passes through points such as (1 comma negative 1), (2 comma negative 4), (negative 1 comma negative 1), and (negative 2 comma negative 4).
C
Image with description On a coordinate plane, the x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. The curve passes through the points (negative 1 comma 0) and (0 comma 1). From (negative 1 comma 0), the curve extends downwards and to the left into the third quadrant, with an arrow indicating it continues indefinitely. From (negative 1 comma 0), the curve also extends upwards and to the right, passing through (0 comma 1) and approaching the horizontal line y = 2 as x increases, with an arrow indicating it continues indefinitely in the first quadrant.
D
Image with description On a coordinate plane, the x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. The curve originates at the point (negative 2 comma 0) on the x axis. It extends upwards and to the right, passing through the points (negative 1 comma 1), (2 comma 2), and (7 comma 3), and continues indefinitely into the first quadrant.
10

Which table represents an exponential function of the form y is equal to b to the x th power when 0 is less than b comma b is less than 1 ?

A
Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 3'; Column 2, '1 over 27' Row 3: Column 1, 'negative 2'; Column 2, '1 ninth' Row 4: Column 1, 'negative 2'; Column 2, '1 third' Row 5: Column 1, '0'; Column 2, '1' Row 6: Column 1, '1'; Column 2, '3' Row 7: Column 1, '2'; Column 2, '9' Row 8: Column 1, '3'; Column 2, '27'
B
Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 2 point 7 5'; Column 2, 'negative 1 point 3 8 6' Row 3: Column 1, 'negative 2 point 5'; Column 2, 'negative 0 point 6 9 3' Row 4: Column 1, 'negative 2'; Column 2, '0' Row 5: Column 1, 'negative 1'; Column 2, '0 point 6 9 3' Row 6: Column 1, '0'; Column 2, '1 point 0 9 9' Row 7: Column 1, '1'; Column 2, '1 point 3 8 6' Row 8: Column 1, '2'; Column 2, '1 point 6 0 9'
C
Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 3'; Column 2, '27' Row 3: Column 1, 'negative 2'; Column 2, '9' Row 4: Column 1, 'negative 1'; Column 2, '3' Row 5: Column 1, '0'; Column 2, '1' Row 6: Column 1, '1'; Column 2, '1 third' Row 7: Column 1, '2'; Column 2, '1 ninth' Row 8: Column 1, '3'; Column 2, '1 over 27'
D
Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 2 point 7 5'; Column 2, '1 point 3 8 6' Row 3: Column 1, 'negative 2 point 5'; Column 2, '0 point 6 9 3' Row 4: Column 1, 'negative 2'; Column 2, '0' Row 5: Column 1, 'negative 1'; Column 2, 'negative 0 point 6 9 3' Row 6: Column 1, '0'; Column 2, 'negative 1 point 0 9 9' Row 7: Column 1, '1'; Column 2, 'negative 1 point 3 8 6' Row 8: Column 1, '2'; Column 2, 'negative 1 point 6 0 9'
11

Which set of ordered pairs could be generated by an exponential function?

A
open paren 1 comma 1 close paren , open paren 2 comma 1 fourth close paren , open paren 3 comma 1 ninth close paren , open paren 4 comma 1 over 16 close paren
B
open paren 1 comma 1 half close paren , open paren 2 comma 1 fourth close paren , open paren 3 comma 1 eighth close paren , open paren 4 comma 1 over 16 close paren
C
open paren 1 comma 1 close paren , open paren 2 comma 1 half close paren , open paren 3 comma 1 third close paren , open paren 4 comma 1 fourth close paren
D
open paren 1 comma 1 half close paren , open paren 2 comma 1 fourth close paren , open paren 3 comma 1 sixth close paren , open paren 4 comma 1 eighth close paren
12

What is the range of the graph of y=((1)/(6))^x−2 ? Enter the range as an inequality. Enter your answer in the box.

Answer:

y>-2

13

Which graph represents an exponential growth function?

A
Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. The curve begins in the second quadrant, running nearly parallel and just above the negative x-axis asymptotically, with an arrowhead pointing directly to the left near "negative 9 comma 0 point 2". Moving right, it slowly curves upward, passes through "negative 1 comma 0 point 5", and crosses the y-axis at the y-intercept "0 comma 1". It then enters the first quadrant, curving sharply upwards and increasing rapidly through "1 comma 2", "2 comma 4", and terminates with an arrowhead pointing toward the top right near "3 comma 9".
B
Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. The curve begins in the second quadrant, rising steeply upwards with an arrowhead pointing towards the top left near "negative 3 point 5 comma 9 point 5". As it moves right, it decreases rapidly, passing through "negative 1 comma 2", crossing the y-axis at the y-intercept " 0 comma 1", and flattening out significantly as it enters the first quadrant. It approaches the positive x-axis asymptotically, running nearly parallel and just above it, and ends with an arrowhead pointing directly to the right near "9 comma 0.3".
C
Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. From the origin, double-headed arrow pointing up towards the origin and the curve bends downwards into the fourth quadrant and extends to the right, passing through approximately "1 comma negative 1", "4 comma negative 2", and "9 comma negetive 3", where it terminates near the right edge of the grid.
D
Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. From the origin, double-headed arrow pointing down towards the origin and the curve rises slowly and extends to the right, passing through approximately "1 comma 1", "4 comma 2", and "9 comma 3", where it terminates near the right edge of the grid.
14

Which set of ordered pairs could be generated by an exponential function?

A
open paren negative 1 comma negative 1 half close paren , open paren 0 comma 0 close paren , open paren 1 comma 1 half close paren , open paren 2 comma 1 close paren
B
open paren negative 1 comma 1 close paren , open paren 0 comma 0 close paren , open paren 1 comma 1 close paren , open paren 2 comma 4 close paren
C
open paren negative 1 comma 1 half close paren , open paren 0 comma 1 close paren , open paren 1 comma 2 close paren , open paren 2 comma 4 close paren
D
open paren negative 1 comma negative 1 close paren , open paren 0 comma 0 close paren , open paren 1 comma 1 close paren , open paren 2 comma 8 close paren
15

Which of the following exponential equations could be represented by the table? x negative 3 negative 2 negative 1 0 1 2 3 4 5 y 2 point 0 0 1 4 2 point 0 0 4 1 2 point 0 1 2 3 2 point 0 3 7 2 point 1 1 1 2 point 3 3 3 3 5 11

A
y is equal to 1 third raised to the x minus 3 power minus 3
B
y is equal to 3 raised to the x minus 3 power plus 2
C
y is equal to 3 raised to the x minus 2 power minus 3
D
y is equal to 1 third raised to the x minus 3 power minus 2
16

Which properties are present in a table that represents an exponential function in the form y is equal to b to the x th power when b is greater than 1 ? I. As the x -values increase, the y -values increase. II. The point open paren 1 comma 0 close paren exists in the table. III. As the x -values increase, the y -values decrease. IV. As the x -values decrease, the y -values decrease, approaching a singular value.

A
II and III
B
I and IV
C
III only
D
I and II
17

What are the domain and range of f of x is equal to 1 fifth to the x th power ?

A
The domain is all real numbers. The range is all real numbers.
B
The domain is all real numbers greater than zero. The range is all real numbers greater than zero.
C
The domain is all real numbers. The range is all real numbers greater than zero.
D
The domain is all real numbers greater than zero. The range is all real numbers.
18

Which graph represents an exponential function?

A
Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The curve originate from the origin and passes through the points 1 comma 3, 2 comma 4, 5 comma 7, and 7 comma 8 in the first quadrant. The arrow is present on both end of curve.
B
Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The graph is made up of two different curves that do not meet. One of the curve decreases rapidly in the second quadrant and passes through the point 0 comma 1 and it goes towards the x axis in first quadrant. The other curve cuts the x axis at point negative 4 comma 0 and then goes rapidly towards the negative side of the y axis in the third quadrant. The arrow is present on both end of two curve.
C
Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The curve passes through the point 0 comma 1, 1 comma 3 and 2 comma 9. It increases rapidly in the first quadrant as x increase and goes towards the y axis as x decreases in the second quadrant. The arrow is present on both end of curve.
D
Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The curve passes through the point negative 2 comma negative 4, the origin, and 2 comma 4. The curve decreases rapidly in the first and the third quadrant and changes direction at the origin. The arrow is present on both end of curve.
19

Which graph represents an exponential decay function?

A
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at the origin (0 comma 0) and extends into the first quadrant. The curve is continuously increasing and appears concave down. It passes through (1 comma 1), (3 comma 2), and (8 comma 3).
B
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), (2 comma 4) and (3 comma 8). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches negative infinity.
C
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at approximately (0 comma 0) and extends to the right in fourth quadrant. The curve is continuously decreasing and it passes through approximately (1 comma negative 1), (4 comma negative 2), and (9 point 5 comma negative 3).
D
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 1 comma 2), (negative 2 comma 4), (negative 3 comma 8), (0 comma 1), (1 comma 0 point 5), and (2 comma 0 point 2 5). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches positive infinity.
20

Which of the following describes the transformation of g of x is equal to 3 times 2 raised to the negative x power plus 2 from the parent function f of x is equal to 2 to the x th power ?

A
reflect across the x -axis, stretch the graph vertically by a factor of 3 , shift 2 units up
B
reflect across the y -axis, stretch the graph vertically by a factor of 2 , shift 3 units up
C
reflect across the y -axis, stretch the graph vertically by a factor of 3 , shift 2 units up
D
reflect across the x -axis, stretch the graph vertically by a factor of 2 , shift 3 units up

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