Math 3 FALL FINAL REVIEW

Chapter 2 - Family Functions and Even/Odd/Neither

100

Which of the following are the asymptotes of 

g(x)=1/_(x+5)  -2 ?

x=-5 and y=-2

200

Is this equation even, odd, or neither?

f(x) = -7x³+4x⁵+x

Odd

300

Find the equation for the word problem below:When Mr. Lee kicked a soccer ball, it traveled a horizontal distance of 150 feet and reached a height of 100 feet at its highest point.  

y=-4/225*(x-75)²+100

400

Make the equation below into graphing form:

y²+16y+x²-6x+48=0

(y+8)²+(x-3)²=25

500

What are the solutions to the following equation?

9x²-11=6x

1 plus or minus 2 square root 3 all divided by 3

Chapter 3 - Systems, Extraneous Solutions, and Simplifying Exponents/Radicals

100

[(zx³y²*x⁰z³)/(2x^-2y²)]³

z¹²x¹⁵/8

200

simplify:

cube root 189m⁶n⁴p⁴

3m²np cube root _7np

300

Solve for x:

square root _(x-3)=x-5

Answers:

(7,2) and x=4 is extraneous solution

400

Solve the system and explain what it means in the context of the graph:

y=1/2*x²+1

y=2x-1

A parabola and a line intersect once at the point of (2,3)

500

Solve the following system:

x²+y²=25

y=x²-13

(-4,3) (4,3) (-3,-4) and (3,-4)

Chapter 5 - Compositions, Inverses, and Exponentials

100

Write the composition of g(f(x))

when f(x) = -2x+7     and        g(x)=x²

g(f(x))=4x²-28x+49

200

Find the inverse equation:

f(x)=1/3*(x+2)³-5

f^-1(x)=cube root 3_(3x+15)  -2

300

Find the inverse, and state any restrictions if necessary.

g(x)=square root_(x+1). +2

g^-1(x)=(x-2)²-1; x greater than or equal to 2

400

What is the asymptote for an exponential function?

y=k

500

Write an equation for an exponential equation that passes through the points (1,23) and (-2,-3) and has an asymptote of y=-4

y=9(3)^x-4

Chapter 7 - Law of Sines/Cosines, Graphing Logarithms

100

Given triangle ABC, find the exact and approximate measurement of Angle A.

Side CA=28

Angle B = 62 degrees

Side BC = 25

Angle A = sin^-1[(25sin62)/28] 

approximately 52.03 degrees

200

Given triangle ABC, find the exact and approximate measurement of side a.

Side CA=14

Angle A = 93 degrees

Side AB = 20

Side A = square root _{(596-560cos93)}

Approximately = 25.01

300

Given triangle ABC, find the exact and approximate measurement of Angle B.

Side AB=12

Side BC = 18

Side CA = 28

Angle B = cos^-1(316/-432) 

approximately 137.01 degrees

400

What is the asymptote of a logarithm function?

x=h

500

Find 4 coordinates of the following log function after all of the transformations:

y=-2log₃(x+7)-4

(-6 and 2/3, -2)

(-6, -4)

(-4,-6)

(2,-8)

Logarithms

100

Find the inverse:

y=1/3(4)^x-5+8

y^-1=log₄(3x-24)+5

200

Condense the logarithm:

2log₃(3x)-{log₃(v⁸)}/2

log₃(9x²/v⁴)

300

Solve for x:

log₃(2x)-log₃(x-5)=4

x=405/79

400

Solve for x with exact and approximate answer:

ln(x-8)=3

e³+8

Approximate:28.09

500

Solve for x:

lnx+ln4x=2

e/2