Final Project

Polynomial Function

100

Find the x and y intercepts of the polynomial function, Y = 3x + 5 

y=5 , x = -5/3

200

Find the x and y intercepts of the polynomial function 

y = x²+4x-24

x = (-4 +- ∫112)/2

300

Find the polynomial function given 3 x-intercepts. 

(-1.618,0) , (-1, 0) , (0.618,0)

x³+2x²-1

400

What is the domain, range, f(x)>0, f(x)<0, and f(x)=0 of the polynomial function? 

y = -∫(x+5) + 2

Domain : [-5, infinity)

Range : (-infinity, 2]

f(x)>0 : [-5, -1)

f(x)<0 : (-1, infinity) 

f(x)=0 : -1

500

Find the two other x-int for the polynomial function, given x-1 is an intercept. 

y = x³ + 3x² - 2

x = (-2 +- ∫12)/2

Rational Functions

100

Find the horizontal and vertical asymptotes and the x/y intercepts for the following equation : x² - 144 / x-3

HA: none  VA: 3  x-int: 12, -12   y-int:48

200

At what point(s) is f(x) increasing and decreasing for the following equation? Also, find the point of the hole in the graph 

inc: never   dec: (-infinity, 0) (0,5) (5, infinity)    hole: (0, -1/5)

300

Draw a graph of the following equation: x-7/x² - 9 

See graph

400

Find the following: Domain, Range, x/y intercepts, when f(x) >/< 0, and when f(x) increasing/decreasing. Also, find the equation of the slant asymptote.

f(x) = x² -100/ x+3

HA:none VA = -3 x-int: 10, -10 y-int: -33.33 D:(-infinity, -3)(-3, infinity) R:(-infinity, infinity) f(x) >0: (-10, -3), (10, infinity) f(x) < 0: (infinity, -10), (-3, 10) inc: same as domain dec: never

SA:y = x+3

500

Draw/label a graph of the following equation:

f(x) = x³ + 3x² -10x /                           x⁴ -6x³ + 15x² -42x + 56

See graph

Exponential and Logarithmic functions

100

Find x: 

log₄16 = x

x = 2

200

Find x: 

3^x = 42

x = 3.402

300

Expand the logarithm: 

ln((7x+5)(y+1))/(x+6)²

ln(7x+5) + ln(y+1) - ln(x+6)

400

Solve for x: 

log(x-8)+log(x+3) = 1

x=(5+sqrt(161))/2

500

Find the exponential equation that goes through these points:

(1, 45), (2, 255), (3, 1515)

y = 7(6)^x+3

Limits and Conic sections

100

What is the center of this ellipse:

(x-2)²/25 + (y+6)²/16 = 1

(2,-6)

200

Find the limit of lim_x->4(x²+x-20)/x-4

x=9

300

Find the equation of the ellipse with vertices (3, 8), (3, 2) and foci points (3, 4), (3,6)

(x-3)²/8 + (y-5)²/9 = 1

400

Find the slant asymptote equations for the following hyperbola with points at (-4, 7), (-4, 13) and (-2,10), (-6,10)

1.5x + 14 and 4 - 1.5x

500

find the limit of lim_{x -> 12}     1/12 - 1/x  / x-12

1/144