Final Review - Precalculus

Functions

100

f(x)=4/x g(x)=3x+9 (fog)(x)

What is 4/(3x+9)

200

Find the inverse function of f f(x)=2x-5

What is (x+5)/2

300

f(x)= 7x if x<0; x+4 if 0<=x<=2; (x-2)^2 if x>=2 Find: f(-7)+f(0)+f(4)

What is -41

400

A ball is thrown across a playing field. Its path is given by the equation below, where x is the distance the ball has traveled horizontally, and y is the height above ground level, measured in feet. y=-0.005x^2 + x + 10 How far has it traveled horizontally when it hits the ground?

What is 210 ft

500

Find the domain of the function f(x) = [(x+8)^(1/2)]/( x-1)

What is -8<=x<1 or x>1

Logarithms

100

Find the solution e^(4x)=19

What is 0.7361 or ln(19)/4

200

Domain of f(x)=log(x^2-1)

What is x<-1 or x>1

300

Expand log[(x^7)/(yz^3)]

What is 7log(x)-log(y)-5log(z)

400

Solve log (x - 7) = 4

What is 10007

500

Solve log 4 + log x = log 6 + log (x-3)

What is 9

Rationals

100

Find the vertical asymptote(s).

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

V.A. x=-3 and x =0

200

Find the horizontal and vertical asymptotes.

(7+x)/(7-x)

V.A. x=7

H.A. y=-1

300

Find the domain of the function.

2/(x^2-3x-18)

Domain: All real numbers x except x = 6, -3

400

Find the slant asymptote.

(24x^2-x-8)/(3x-2)

8x+5

500

Find all asymptotes and holes of the graph:

f(x)=(2x^2-7x+3)/(2x^2-3x-9)

V.A.: x=-3/2

H.A.: y=1

Hole at x =3

Polynomials

100

Factor 10x^2 - 27x + 18

What is (5x - 6)(2x - 3)

200

solve for x

 x³ + 4x² + 8x + 32 is this.

x = 2i√2, -2i√2, -4

300

Solve for y

5y^3 - 45y + 3y^2 - 27

y= -3, 3, -3/5

400

Solve the following quadratic equation by using the quadratic formula:

5x^2-30x+15=0

3 pm (sqrt(6))

500

Solving 

2x⁴ - 19x² + 45=0

x=√5, -√5, (3√2)/2, -(3√2)/2

Random

100

what is tangent at 3Π/4

1

200

If a line y = mx + b is parallel to y = 3x + 4 and goes through the point (1, 1), then what is b?

-2

300

Solve the system of equations. 2x^2-y^2=1 x+y=12

What is (5,7) and (-29,41)

400

If a line y = mx + b is perpendicular to 4x - y = 8 and goes through the point (-4, 20), then what is b?

19

500

Solve the system of equations. x^2-y^2=5 x^2+y^2=13

What is (3,2), (3,-2), (-3,2), and (-3,-2)