AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Solving Exponential and Logarithmic Equations

Solving Exponential and Logarithmic Equations — Unit test Answers

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The graph of a quadratic function, , is reflected over the x-axis. Which of the following is the equation of the transformed graph?

Question illustration
A
y = negative x squared
Option A
B
y = (negative x) squared
Option B
C
y = StartRoot negative x EndRoot
Option C
D
y = negative StartRoot x EndRoot
Option D
2
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How is the graph of the parent function of transformed to produce the graph ?

Question illustration
A
It is horizontally stretched by a factor of .
Option A
B
It is vertically stretched by a factor of .
Option B
C
It is translated left by unit.
Option C
D
It is translated right by unit.
Option D
3

Based on the family the graph below belongs to, which equation could represent the graph?

Question illustration
A
y = 0.6 Superscript x Baseline minus 2
Option A
B
y = 0.6 x squared minus 1
Option B
C
y = negative 0.6 x cubed minus 1
Option C
D
y = log (x) minus 2
Option D
4

The graph of is shown.Which is the graph of ?

Question illustration
A
On a coordinate plane, a cubic root function is shown. It approaches x = negative 3 in quadrant 3, has an inflection point at (negative 1, negative 2), and then approaches y = 2 in quadrant 1. It crosses the y-axis at (0, negative 2).
Option A
B
On a coordinate plane, a cubic root function is shown. It approaches x = negative 1 in quadrant 3, has an inflection point at (2, 1), and then increases and approaches y = 5.
Option B
C
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 4, increases, has a point of inflection at (2, 1), and then increases and approaches x = 4.
Option C
D
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 2, decreases, has a point of inflection at (negative 2, 1), and then decreases and approaches x = negative 4.
Option D
5

The value of a graphed function doubles for each increase of 1 in the value of x. Which of the following could be the parent function of the graphed function?

A
y = 2 Superscript x
Option A
B
y = x squared
Option B
C
y = StartAbsoluteValue x EndAbsoluteValue
Option C
D
y = StartRoot x EndRoot
Option D
6

Which equation describes how the parent function, , is vertically stretched by a factor of 4?

Question illustration
A
y = x cubed + 4
Option A
B
y = (x + 4) cubed
Option B
C
y = 4 x cubed
Option C
D
y = x Superscript 4
Option D
7

The graph of the function is shown.Which graph represents the function ?

Question illustration
A
On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (1, 2) and (2, 1). The other curve opens down and to the left in quadrant 3 and goes through (negative 2, negative 1) and (negative 1, negative 2).
Option A
B
On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (2, 2.5). The other curve opens down and to the left in quadrants 2 and 3 and goes through (negative 0.5, 0) and (negative 2, 1.5).
Option B
C
On a coordinate plane, 2 curves have an asymptote at y = negative 2. On curve opens up and to the right in quadrants 1 and 2 and goes through (negative 1, 1) and (0, 0.5). Another curve opens down and to the right in quadrant 3 and goes through (negative 3, negative 1) and (negative 2.5, negative 2).
Option C
D
On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (0.5, 1) and (1, 0.5). The other curve opens down and to the left in quadrant 3 and goes through (negative 1, negative 0.5) and (negative 0.5, negative 0.5).
Option D
8

The graph below belongs to which function family?

Question illustration
A
linear
B
quadratic
C
cubic
D
absolute value
9

A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function transformed to create the graph of the function ?

Question illustration
A
It is a vertical stretch with a factor of 100 and a translation 5 units right.
B
It is a vertical stretch with a factor of 95.
C
It is a vertical stretch with a factor of 100 and a translation 5 units down.
D
It is a vertical stretch with a factor of 500.
10

The velocity of a particle can be modeled by the function . Which graph accurately shows the velocity of the particle at any time, t?

Question illustration
A
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2.5, negative 2), and then increases into quadrant 2 and approaches x = negative 1.
Option A
B
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, negative 2), and then increases into quadrant 1 and approaches x = 4.
Option B
C
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, 2), and then decreases into quadrant 4 and approaches x = 5.
Option C
D
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function starts in quadrant 4 and increases into quadrant 1. It has a point of inflection at (8, 2) and then it continue to increase in quadrant 1.
Option D

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