Functions and Transformations
Rational Functions
Exponentials and Logarithms
Trig Part 1
Trig Part 2
100
True or False: A single point that is NOT the top or bottom of a bump can be an absolute maximum
True
100
Find all vertical asymptotes:
f(x)=3/((x-2)(x+3)(x-5))
x=2, x=-3, x=5
100
For what values of x is f(x)=log(x) not defined?
x <= 0
100
Convert the following from radians to degrees:
pi/6, pi/4, pi/3
pi/6 = 30
pi/4 = 45
pi/3 = 60
100
Define amplitude
Distance from highest/lowest point to the midline
200
Picture the graph of x3. How many intervals of increasing are there and what are the intervals?
one!
(-\infty, \infty)
200
Draw on the whiteboard a vertically stretched and horizontally compressed apple. Comment on what you notice.
Ms. Dror assesses correct solution, both apples should look the same!
200
Solve for x:
2^(x-3)=2^4
x=7
200
Solve sec(60 deg)
2
200
Roughly sketch one cycle of the parent negative sine curve and one cycle of the parent negative cosine curve.
Ms. Dror will assess.
300
Describe ALL transformations performed on this equation:
f(x)=-(2x+3)^2-10
1. Reflection over the x-axis
2. Horiz comp by 1/2
3. Left 3
4. Down 10
300
Determine all vertical asymptotes of the following:
f(x)=[x^2-x-6]/[(x-3)(x+2)(x-4)]
x=4
There are two holes at x=3, x=-2
300
Solve the following expression.
log_9(1/3)
-1/2
300
Solve sin(300 deg)
-sqrt(3)/2
300
What is the period, starting, and ending point of the following:
y=sin3(x+pi/3)
period: (2pi)/3
start: -pi/3
end: pi/3
400
f(x)=1/(x-2), g(x)=sqrt(x+4), h(x)=x^2-5
Find h(g(f(x)))
1/(x-2)-1
400
Determine the horizontal asymptote of the following:
f(x)=[3(x-1)^4(x+5)(x-4)]/[2(x-4)^4(x+3)^2(x-7)(x+1)]
y=0
(smaller degree)/(larger degree)
400
Solve the equation:
log(x)-log(2)=1
x=20
400
Solve
cos((11pi)/6)
sqrt(3)/2
400
At what points do the parent sine and cosine curves intersect?
(pi/4, 1/(sqrt(2)))
500
Find the inverse of the following function:
f(x)=(3x+5)/(2x-7)
f^(-1)(x)=(7x+5)/(2x-3)
500
Consider a rational that has a degree 4 poly in the numerator and a degree 3 poly in the denominator. There is no horizontal asymptote. Think about polynomial division. What kind of end behavior will this rational function following.
Degree 4 divided by degree 3 is degree 1.
It will follow a linear end behavior.
500
Solve the equation:
e^(2x)-3e^x-28=0
x=ln(7)
500
Solve cot(540 deg)
undefined
500
Consider the curve below that models simple harmonic motion of a pendulum swinging.
Determine the frequency of the following curve and define what the frequency is.
y=4sin(40pi)(t-3)+2
40, 40 cycles per second.