Final Project

Polynomial Functions

100

What is x for

12x + 7 = 5

x = -1/6

200

What are the x-intercepts for

y = x² + 4x - 12?

x = -6, 2

300

What are the x-intercepts for 

y = x³ - 9x² + 23x - 15?

x = 1, 3, 5

400

What is the exponential equation of a function if points (0,2), (2,18), and (1,6) exist on it?

y = 3(2)^x

500

What are the x-intercepts for 

y = x⁵ - 10x⁴ +17x³ + 76x² -228x + 144

x = 2, -3, 4, 1, 6

Rational Functions

100

Find x & y intercepts

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

x-int: (-2, 0)

y-int: (0, 2)

200

Find the vertical asymptote of y = 16/(2x-7)

x = 3.5

300

Find the horizontal asymptote of

(x-4)(x+6)/(2x+7)

no HA

400

Find the slant asymptote of

(x²-6x)/(x+2)

y = x - 8

500

Find VA, HA, x-int, and y-int of:

f(x)= (4x²-36)/(x²-x-12)

VA: x=4

HA: y=4

x-int: (3,0)

y-int: (0,3)

Exponential and Logarithmic functions

100

Find the horizontal asymptote and y-int

y= 3(¾)^x + 10

HA: y = 10

y-int: (0, 13)

200

Solve for x

 Log8(x+2)-log8(x)=log8100

x=0.02

300

Solve for x

ln(6x+3)-ln8=10

x=29368.2

400

What interest rate do you need if you invest $9,000 and get a return of $40,000 for 25 years?

r=1.46 or about 1.5%

500

Solve for x

e^2x-10e^x+24=0

x=1.38   x=1.79

Limits and Conic sections

100

Find the Center 

(x-5)²/36 + (y+8)²/9 = 1

(5, -8)

200

Evaluate the limit 

lim_x-->0x²-9/x²-5x-24

3/8

300

Find the foci points 

(x-4)²/25 + (y+3)²/9 =1

(8, -3) and (0,-3)

400

What are the center and vertices of the hyperbola?

8x² - 2y² + 16x -12y + 8 = 0

Center: (-1, -3)

Major Vertices: (-1,-6) (-1,0) 

Minor vertices: (0.5, -3) (-2.5,-3)

500

Evaluate the limit: 

Lim_h-->0

f(x+h)-f(x)/h

f(x)= √(x+8)

1/2√(x+8)