Precalculus review

Unit 1A-1B

100

For the function s(t), s is the number of people swimming at the local pool and t is the temperature measured in fahrenheit. Identify the dependent and independent variables.

Dependent:

Independent:

Dependent: The number of people swimming.

Independent: The temperature (in Fahrenheit).

200

What is the average rate of change for each function on the given intervals?

y=3x^2-2x+1 on -1<=x<=2

y(-1)=3+2+1=6

y(2)=12-4+1=9

(9-6)/(2--1)=3/3

answer=1

300

Find the leading coefficient and the degree of each polynomial.

F(x)=x⁵ -2x²   

Answer L.C :1

Answer Degree:5

400

Transformations

Algebraically

F(x)=6-4x²

g(x)=f(x)+5 find g(x)

g(x)=11-4x²

500

f(x)=2x²-3x+1

g(x)=f(2x)+3, Find g(x)

g(x)=8x²-6x+4

Unit 2A

100

Could the function represent a linear function, exponential function or neither?

(3,6), (4,11), (5,16)

Linear 

200

In the exponential function f(x)=8(1.9)^x increasing or decreasing?

Increasing 

300

The Function f is given by f(x)=log(3-x)+2. Find the information below for f.

Asymptote:

Domain:

Asymptote: x=3

Domain: (-∞, 3)

400

What is equivalent expression to log((a²b²)/(c⁴))

log a²+logb²-logc³
or
2log a +2log b -3log c

500

Let f(x)=3x²-4x+5 and g(x)=5-3x

Find f(g(-1)).

F(g(-1))=37

Unit 2B

100

The function f is given by f(x)=3log₂(x)+8. Find f^-1(x).

F^-1(x)=2^((x-8)/(3))

200

What is Log₃243?

x=5

300

What is the solution to the equation 4*2^(x+5)-10=22

-2=x

400

logx+log(x-3)=1. Solve for x

X=5, x=-2

answer: x=5 

log(-2) is not real

500

e^(2x-1)+68=207

x=((ln139+1)/(2)) estimate=2.967

Unit 3A

100

Sin 3pi/2

-1

200

The measurement of an angle in standard position is listed. In which quadrant is the terminal ray.                                        

𝜃=2.9pi

                                   

    

-2pi=0.9pi

Quadrant 2

300

The function is given by f(𝜃)=cos𝜃 . Describe the concavity of f on the interval, and if f is increasing or decreasing on the interval

 pi/2 <𝜃<pi

                                   

    

concave up 

Decreasing

400

sin(-5pi/4)

(sqr2/2)

500

State the amplitude, period, phase shift, and vertical shift.

y=3cos(5x-pi)

Amp:

Midline:

Max value:

Phase shift:

Period: 

Freq:

min value:

Amp:2

Midline:y=0

Max value:3

Phase shift:right pi/5

Period: 2pi/5

Freq:5/2pi

min value:-3

Unit 3B

100

In the xy plane, the angle 𝜃 is in standard position. WHat is the slope of the terminal ray of the angle?

𝜃=5pi/3

                                   

    

                                   

    

-square root of 3

200

In the x-y plane, the angle 𝜃 is in standard position. WHat is the slope of the terminal ray of the angle?

𝜃=3pi/4

-1

300

Evaluate

tan(pi/2)

sin𝜃/cos𝜃

1/0 =undefined

400

Evaluate the following expressions. Find the principal value in radians. NO CALCULATOR!!

tan^-1(-1)

-pi/4

500

Solve each equation for 0<=x<=2pi. Find the exact value(s) using the unit circle.

-1=cos²x+2cosx

x=pi