Answers 2022 Algebra II B SSSolving Exponential and Logarithmic Equations

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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?

y = negative x squared

y = (negative x) squared

y = StartRoot negative x EndRoot

y = negative StartRoot x EndRoot

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How is the graph of the parent function of transformed to produce the graph ?

It is horizontally stretched by a factor of .

It is vertically stretched by a factor of .

It is translated left by unit.

It is translated right by unit.

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

y = 0.6 Superscript x Baseline minus 2

y = 0.6 x squared minus 1

y = negative 0.6 x cubed minus 1

y = log (x) minus 2

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

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).

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.

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.

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.

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?

y = 2 Superscript x

y = x squared

y = StartAbsoluteValue x EndAbsoluteValue

y = StartRoot x EndRoot

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

y = x cubed + 4

y = (x + 4) cubed

y = 4 x cubed

y = x Superscript 4

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

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).

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).

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).

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).

The graph below belongs to which function family?

linear

quadratic

cubic

absolute value

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 ?

It is a vertical stretch with a factor of 100 and a translation 5 units right.

It is a vertical stretch with a factor of 95.

It is a vertical stretch with a factor of 100 and a translation 5 units down.

It is a vertical stretch with a factor of 500.

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

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.

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.

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.

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.

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