Polynomials &
Rationals
Rationals
Exponentials &
Logs
Logs
Conics
Sequences & Series
Limits
100
Describe the end behavior of
y=2x^5+3x^2-2x+1
y \rightarrow \infty as x \rightarrow \infty and y \rightarrow -\infty as x \rigtharrow -\infty
100
Find the domain, range and any asymptotes of
y=ln (x-2)
Domain: All real numbers greater than 2
Range:
(-\infty,\infty)
Asymptotes: x=0
100
Find the vertex and focus of the parabola:
Vertex (0,0)
Focus (2,0)
100
\sum_{i-2} ^5 i^2-2
Find the sum:
46
100
Find the limits using the graph:
a) \lim_{x \to 2^- } f(x)
b) \lim_{x \to 4 } f(x)
a) -2
b) 4
200
List all possible rational roots:
y=-2x^5-4x^4-13x^3+70x^2-90x+14
\pm14 , \pm7 , \pm 7/2 , \pm2 , \pm1
200
Evaluate the log:
log_4 (\frac{1}{64})=
-3
200
Find the equation of the conic shown here: 
Hyperbola.
\frac{x^2}{64} - \frac{y^2}{17}=1
200
Write a rule for the sequence: 9, 14, 19, 24
a_n=5n+4
200
Use a table to find the limit as x approaches 0 of
y=\frac \sin x \x
1
300
Find all horizontal and vertical asymptotes of the function:
r(x)=\frac{x^2}{x^2-11x+30}
y=1, x=5 and x=6
300
Combine into a single logarithm:
\log_2 x + \log_2 (xy^2) +4log_2 y
\log_2 (x^2 y^6)
300
Sketch the graph of the ellipse:
\frac{(x-3)^2}{9} + \frac{y^2}{36}=1
300
Find the first 3 partial sums of the series: 20+10+5+...
S_1=20
S_2=30
S_3=35
300
Find the limits below if
f(x)=\frac {3x^2+3x-6}{x^2-4}
a) \lim_{x \to -2 } f(x)
b) \lim_{x \to \infty } f(x)
a) 9/4
b) 3
400
Use synthetic division to show (x-4) is a factor of
f(x)=x^5+x^4-36x^3-16x^2+320x
See board
400
Solve the equation:
3^{x+2} = 5^{2x}
x = 1.036
400
Complete the square and determine the type of curve represented by the equation:
4x^2+9y^2+24x-36y+36=0
Ellipse
\frac{(x+3)^2}{9} + \frac{(y-2)^2}{4}=1
400
During a baseball season, a company pledges to donate $5000 to a charity plus $100 for each home run hit by a local team. Does this represent a sequence or series? Explain.
Series
400
Suppose f(x) is a function, where
f(2)=3
Does this imply:
\lim_{x \to 2} =3?
No. Consider a piecewise function
500
Write the equation of the cubic function shown here:
y=-\frac{1}{2}(x+1)(x+4)(x-3)
500
How long will it take an investment of $300 to triple if the interest rate is 9.5% per year, compounded continuously?
About 11.5 years
500
A cannon fires a cannonball along a parabolic path with vertex at the highest point of the path.
If the cannonball lands 1600 ft from the cannon and the highest point it reaches is 2,400 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon.
(x-800)^2= -\frac{800}{3} (y-2400)
500
Find the sum of the positive odd integers less than 300.
Hint - use a formula
22,500
500
Find the limit using any method:
\lim_{x \to 0} \frac{|x-4|}{x-4}
DNE