Answers 2025-2026 FBISD - Precalculus A CRUnit Test

Unit Test — Unit test Answers

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Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.

Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.

Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.

Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.

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Which expression is equivalent to 30°?

Inverse of cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Inverse of sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)

Review the graph.

y = –3cos(x)

y = –3sin(x)

y = 3cos(x)

y = 3sin(x)

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

It is the graph of y = sec(x) shifted 3 units right and 7 units up.

It is the graph of y = sec(x) shifted 3 units left and 7 units up.

It is the graph of y = sec(x) shifted 3 units left and 7 units down.

It is the graph of y = sec(x) shifted 3 units right and 7 units down.

The function g(x) represents f(x) = after translating units left and 4 units up.Which equation represents g(x)?

g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) minus 1

g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) + 7

g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) minus 1

g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) + 7

What is the period of the function ?

units

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).

On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).

Review the graph.

y = tanx

y = cosx

y = tan-1x

y = cos-1x

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

3.2

5.6

6.4

13.0

A particle travels in a circle around a fixed point at 16 revolutions per minute. The linear velocity of the particle is 240π inches per minute.What is the distance, in inches, between the particle and the fixed point?

3.75

7.5

Which of the following is the equation of the function below?

y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.

y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.

y equal to 0 point 5 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.

y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.

Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?

–2

Negative one-half

One-half

Over which interval is the graph of y = cos(x) strictly increasing?

0 less-than x less-than StartFraction pi Over 2 EndFraction

0 < x < π

StartFraction pi Over 2 EndFraction less-than x less-than StartFraction 3 pi Over 2 EndFraction

π < x < 2π

Which is an x-intercept of the graph of the function ?

(minus StartFraction 2pi over 3 EndFraction , 0)

(minus StartFraction pi over 3 EndFraction , 0)

(StartFraction pi over 6 EndFraction , 0)

(StartFraction 5pi over 6 EndFraction , 0)

Consider the function y = cos(x). Which change would increase the period by a factor of 3?

Multiply cos(x) by

Multiply cos(x) by 3.

Multiply x by

Multiply x by 3.

What is the equation of the graph below?

y = sec(x) + 2

y = csc(x) + 2

y = csc(x + 2)

y = sec(x + 2)

Which functions are symmetric with respect to the origin?

y = arcsinx and y = arccosx

y = arccosx and y = arctanx

y = arctanx and y = arccotx

y = arcsinx and y = arctanx

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

50 feet

feet

100 feet

feet

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 hours.After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.

2.2 hours

6.3 hours

12.1 hours

12.5 hours

Which of the following is the graph of ?

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 by 2 at (3 pi by 2, comma negative 3 by 2 ) and (negative pi by 2 by negative 3 by 2) and y equals negative 5 by 2 at ( pi by 2 comma negative 5 by 2) and (negative 3 pi by 2 comma negative 5 by 2).

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (3 pi by 2 comma negative 1) and (negative pi by 2 comma negative 1) and y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3).

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (pi comma negative 1) and (negative pi comma negative 1) and y equals negative 3 at (0 comma negative 3).

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 point 8 at (0 comma negative 1 point 8) and y equals negative 2 point 2 at (pi comma negative 2 point 2) and (negative pi comma negative 2 point 2).

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