Final Review!

Unit 1

100

Solve the inequality. Write the solution set in interval notation.

|x-4|<18

(-14, 22)

200

Find the domain and range for the given relation and state whether it is a function.

(1,4),(2,5),(3,6),(4,7)

Domain: {1,2,3,4}

Range: {4,5,6,7}

It is a function!

300

Write the equation with function notation f(x)

-x+3y=-6

f(x)=(1/3)x-2

400

Write an equation for the line described. 

Perpendicular to -x+3y=-6 and through the point (-3,-3)

y=-3x-12

500

Solve the following system of equations.

7x-4y=-7

x+y=-1

(-1,0)

Unit 2

100

Find the product. Write your answer in standard form.

(9-i)(8+4i)

76+28i

200

Solve the equation for x

(x+11)²=-40

x=-11+2i(sqrt(10)), -11-2i(sqrt(10))

300

Solve the equation for x.

x²+3x+5=0

x=-3/2+i(sqrt(11))/2, -3/2-i(sqrt(11))/2

400

Solve by completing the square. Specify what you are adding to both sides.

x²-8x-22=6

Add 16.

x=4+2(sqrt(11)), 4-2(sqrt(11))

500

Solve x²-x-12<0 and put your answer in interval notation

(-3,4)

Unit 3

100

Use synthetic division to perform the division. Express the polynomial in the form f(x)/g(x)=q(x)+r/g(x)

(3x⁴-2x³-10x²+15)/(x-2)

(3x⁴-2x³-10x²+15)/(x-2)=(3x³+4x²-2x-4)+7/(x-2)

200

For the polynomial, one zero is given. Find all others.

f(x)=4x³-x²-4x+1: k=1

x=1/4,1

300

Find the horizontal asymptote of the given function.

f(x)=(x-2)/(x-4)

y=1

400

Solve the following rational equation for x.

1/(x-8)-1=7/(x-8)

x=2

500

Find a polynomial function f of least degree having the graph shown.

f(x)=-(x+2)(x-1)²

Unit 4

100

f(x)=3x+4 g(x)=4x+3

Find f(g(x))

f(g(x))=12x+13

200

Write an equation for the inverse function.

f(x)=-6x-8

f^-1(x)=(x+8)/-6

300

Solve the equation

9^x-1=27^x+3

x=-11

400

Solve for x

log_x4=-2

x=1/2

500

How long will it take for $1786 to grow to $2063 at 2.6% with interest compounded continuously?

It will take 5.55 years.

Variety

100

Is the vertex of f(x)=-x²+3x-15 the highest or lowest point?

Highest

200

Give the range of the following function.

f(x)=(x-2)²+6

[6, infinity)

300

Solve the following rational inequality. Put your answer in interval notation.

(x-6)/(x+3)>0

(-infinity,-3)U(6,infinity)

400

Solve the following equation for x.

x-sqrt(4x+12)=0

x=6

500

Find a possible equation for the function with a graph having the given features.

x intercepts: (-3,0) and (3,0)

y intercept: (0,9/2)

vertical asymptote: x=2, x=-2

horizontal asymptote: y=2

f(x)=(2(x+3)(x-3))/((x+2)(x-2))