Pre-Calc Final

Polynomial Functions

100

Factor 15x²+57x+36

(5x²+4)(3x²+9)

200

Factor x⁴-256

(x-4)(x+4)(x²+16)

300

Find the values of x: (x)²(x-5)(4x²-8x-21)

x = 0, 5, 7/2, and -3/2

400

Find all values of x and determine when the graph goes up and down: x³-7x-6

X = -2, 3 and 1

Everything passes though, there's no bounces

500

Find all values of x:  x⁴+10x³+3x²-166x-280

x = -7, -5, 4 and -2

Rational Functions

100

Find the horizontal asymptote for the following function

f(x) = 3x-5/x²-8x+15

y = 0

200

Find the horizontal asymptote for the following function

f(x) = 5x²-25/3x²+3x-4

y = 5/3

300

Find the vertical asymptote for the following function

f(x) = 27x+3/x²+9x+20

4,5

400

Find the hole in the graph

f(x) = x+5/x²-25

x = 5

500

Find the slant asymptote

f(x) = x²-6x+7/x+5

y = x - 11

Conics and Limits

100

Find the center, vertices and foci points for the ellipse: (x+2)²/25 + (x-6)²/4 = 1

Center: (-2,6)

Vertices: 

Major →(-7,6)(3,6)

Minor →(-2,4)(-2,8)

Foci: 

(-2 +/- √21, 6)

200

Evaluate the limit: lim x→1 (2x²-3x-1)/(3x-1)

3

300

Find an equation for a hyperbola with vertices (2,4) (12,4) and passes through (20,8)

(x-7)²/(25) - (y-4)²/(25/9) = 1

400

Find the center, vertices, and foci points for the hyperbola: 2x²-3y²+4x-9y-14=0 

Center: (-1, -1.5)

Vertices: 

Major → 

(-1, -1.5 +/- √(5/3))

Minor→ 

(-1 +/- √-5/2, -1.5)

Foci: 

(-1, -1.5 +/- √(25/6))

500

Evaluate the limit: lim →∞

√(x²-2)+3x

∞

Exponential and Logarithmic Functions

100

What is the starting value in a_n=2(3)^n-1

²

200

What is the sum of the first 10 numbers in the geometric sequence an = 3(3)^n-1

88572

300

Find three rational points from the equation y = 2log₂(x+2)+25 c

(-1, 2), (0,3), (2,4)

400

Create a logarithmic equation from the points (5,2), (6,3) and (8,4)

y = log₂(x-4)+2

500

Create a logarithmic equation from the points (-3,-1.5), (3,-0.5) and (27,0.5)

y = log₄(x+5)-2