Answers S1S-OC Pre-Calculus A E3700 - AGUnit Test

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Consider the function.f(x) = x2 + 3Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?

f(x) domain: x ≥ 3f–1(x) domain: x ≥ 3

f(x) domain: x ≥ 3f–1(x) range: y ≥ 3

f(x) domain: x ≥ 0f–1(x) domain: x ≥ 0

f(x) domain: x ≥ 0f–1(x) range: y ≥ 0

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Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?

2.4 hours

2.5 hours

3.0 hours

4.0 hours

Review the graph of complex number z.

(cos(135°) + isin(135°))

(cos(135°) + isin(135°))

(cos(225°) + isin(225°))

(cos(225°) + isin(225°))

Harlon wrote the equation to find the area of a rectangle that has a length of and a width of 18. He solved for x and got Which of the following is an equivalent equation for x?

x = plus-or-minus StartRoot StartFraction uppercase A minus 18 Over 18 EndFraction EndRoot

x = plus-or-minus StartRoot StartFraction uppercase A + 18 Over 18 EndFraction EndRoot

x = plus-or-minus StartRoot uppercase A minus 36 EndRoot

x = plus-or-minus StartRoot uppercase A + 36 EndRoot

A cliff diver leaps from a 100-foot cliff into the Pacific. The diver’s height above the water is modeled by the functionP(x) = –16x 2 + 10x + 100, where x is time in seconds.During which interval is the diver at least halfway down?

2.0 < x < 2.1 seconds

2.1 < x < 2.8 seconds

3.0 < x < 3.4 seconds

3.4 < x < 3.5 seconds

The formula for the volume of a pyramid is Which of the following equations is equivalent to the given formula?

uppercase B = StartFraction 3 uppercase V Over h EndFraction

uppercase B = StartFraction 3 h Over uppercase V EndFraction

uppercase B = StartFraction uppercase V minus one-third Over h EndFraction

uppercase B = StartFraction uppercase V + one-third Over h EndFraction

Which graph represents the function y = cos(4x)?

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 1).

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 1).

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 0).

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 0).

A certain population is modeled by the function . How long will it take for the population to reach 30,000 organisms?

approximately 0.4 years

approximately 0.8 years

approximately 3.6 years

approximately 8.1 years

Identify the horizontal and vertical asymptotes, if any, for the graph of f(x) shown. Check all that apply.

y = 0

y = 1

x = 1

x = –1

no vertical asymptotes

no horizontal asymptotes

Which statements comparing the graphs of function 1 and function 2 are true? Check all that apply.

Function 1 has a hole, while function 2 does not.

Function 1 has an oblique asymptote, while function 2 does not.

Function 2 has a hole, while function 1 only has asymptotes.

Function 2 only has asymptotes, while function 1 has a hole.

Both functions have the same domain restriction.

Both functions have the same vertical asymptote.

Which is equal to –214°?

radians

Review the table of values for function w(x).

–0.75

–0.2

The equation M = 0.6666 log x – 3.2 represents the magnitude of an earthquake depending on the energy it produces. What does 0.6666 represent?

the growth factor

the value of M when x equals 1

the magnitude of the earthquake

the energy produced by the earthquake

The formula to determine energy is . What is the formula solved for v?

v = plus-or-minus StartRoot StartFraction m Over 2 uppercase E EndFraction EndRoot

v = 2 uppercase E minus m

v = plus-or-minus StartRoot 2 uppercase E minus m EndRoot

v = plus-or-minus StartRoot StartFraction 2 uppercase E Over m EndFraction EndRoot

Celo used the simple interest formula to calculate the interest he earned on his savings last month. Which equation is equivalent to the simple interest formula?

uppercase P = StartFraction uppercase A Over 1 + r t EndFraction

uppercase P = StartFraction 1 + r t Over uppercase A EndFraction

uppercase P = uppercase A minus (1 + r t)

uppercase P = uppercase A + (1 + r t)

What is the solution to x 4 + 4x 3 ≤ 12x 2?

(–6, 2)

[–6, 2]

(–ꝏ, –6) U (2, ꝏ)

(–ꝏ, –6] U [2, ꝏ)

Which property of multiplication is shown below? If x = 3 + 4i and y = 5 + 6i, x × y = y × x.

commutative property

identity property

distributive property

associative property

For two complex numbers z and w, which diagram shows the geometric representation of zw?

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 goes to point z, a line with length r 1 + r 2 goes to point z w, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 minus theta 2.

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 goes to point z, a line with length r 1 r 2 goes to point z w, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 minus theta 2.

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 + r 2 goes to point z w, a line with length r 1 goes to point z, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 + theta 2.

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 r 2 goes to point z w, a line with length r 1 goes to point z, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 + theta 2.

For which rational expression is –5 an excluded value of x?

mc016-1.jpg

mc016-2.jpg

mc016-3.jpg

mc016-4.jpg

What are the excluded values of x for ?

x = –1, x = 0, x = 1

x = –1, x = 0

x = 0, x = 1

x = –1, x = 1

Which is the graph of y =-3 ?

On a coordinate plane, a curve starts at (0, 0) and curves up through (negative 3, 3).

On a coordinate plane, a curve starts at (0, 0) and curves down through (1, negative 1) and (4, negative 2).

On a coordinate plane, a curve starts at (0, 0) and curves down through (1, negative 3).

On a coordinate plane, a curve starts at (0, 0) and curves up through (1, 3) and (2, 4.5).

Rectangular coordinates and polar coordinates both represent the same complex number z.Which set of equations demonstrates why both sets of coordinates represent the same number?

r = StartRoot 3 EndRoot + StartRoot 3 EndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi over 4 EndFraction

r = StartRoot 3 EndRoot + StartRoot 3 EndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (StartRoot 3 EndRoot) = StartFraction pi over 4 EndFraction

r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi Over 4 EndFraction

r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (StartRoot 3 EndRoot) = StartFraction pi Over 4 EndFraction

Review the four points on the complex plane.

point A

point B

point C

point D

Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?

The oblique asymptote for g(x) is steeper than for f(x).

Both functions have the same oblique asymptote.

The oblique asymptote for f(x) is steeper than for g(x).

Both functions have parallel oblique asymptotes.

Which pair of related inequalities can be graphed to find the solution set to log(x + 90) ≥ 7?

y ≥ log(x + 90) and y ≤ 7

y ≥ log(x + 90) and y ≥ 7

y ≤ log(x + 90) and y ≤ 7

y ≤ log(x + 90) and y ≥ 7

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