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Just the Basics
Perfect Parabolas
What's the Inverse?
Extra Special Logs
What's an asymptote?
100

Starting with the basic cube function, write an equation for the following transformations: reflection over the x-axis, shifted horizontally left by 4 units, shifted vertically up by 5 units, and stretched by a factor of 2.

y=-2(x+4)^3+5

100
Use the function, f(x) = x^2 – 2x -15 to answer the following: Determine the concavity of f(x).
concave up
100
Find the inverse if f(x)= (2x-3)/4
f^-1(x)=(4x+3)/2
100
Evaluate the logarithm: log5 1
0
100
Given the function, f(x)=(x+1)〖(x-2)〗^2 (x+3) State the degree
4
200
Using f(x) = -2(x-4)^2 + 6 state the intervals in which f is increasing and/or decreasing
inc: (-infinity, 4) dec: (4, infinity)
200
Use the discriminant to determine the number of solutions and type of solutions for the equation: 4x^2-3x+7=0.
discriminant: -103 no real solutions two imaginary solutions
200
Given f(x) = 2x^2-x-4 and g(x) = x+6: Find ( f/g ) (-2).
3/2
200
Solve for x: 2 = 12 – 2 ln(8.1x)
x=(e^5)/8.1 = 18.32
200
Given the function, f(x)=(x+1)〖(x-2)〗^2 (x+3): State the end behavior
both ends go up
300
Answer using the function: f(x) = -3 + √(x+4) state the domain state the range
domain: [-4, infinity) range: [-3, infinity]
300
(5+3i)(3-4i)
27-11i
300
Given f(x) = 2x^2-x-4 and g(x) = x+6: Find (g o f)(x).
2x^2-x+2
300
A typical beehive contains 20,000 insects. The population can increase in size by a factor of 2.5 every 6 weeks. Write the basic exponential growth or decay function.
P(t)=20000(2.5)^(t/6)
300
Given the rational function, f(x) = (x^2-x-6)/(x^2-9), find the vertical asymptotes
x=-3
400
Solve the following absolute value equation: 2|x-4|+3=9.
x= 1, 7
400
Solve the quadratic inequality: -2x^2-13x+24≥0. State your answer in interval notation.
[-8, 1.5]
400
A person’s weight on the moon is approximately one sixth of the weight on Earth. If a person’s weight on Earth is represented by the variable w, then the function that represents the weight on the moon in terms of the weight on Earth can be given as f(w) = 1/6 w. Find the inverse of the function f(w).
f^-1(w)=6w
400
Suzanne wants to invest $20,000 in an account for 25 years at an interest rate of 2.75% compounded monthly. Find the accumulated amount in the account at the end of 25 years.
20000(1+.0275/12)^(12*25)=39,743
400
Given the rational function, f(x) = (x^2-x-6)/(x^2-9), find the horizontal asymptote.
y=1
500
Solve the absolute value inequality: 5+2|2x-4|≥11. Write your answer in interval notation.
(-infinity, 1/2] U [7/2, infinity)
500
Alexander’s catapult will launch an object. The equation below describes the height of the object. h(t)= -4.9t^2+22t+1 What is the maximum height of the object in meters?
25.7 meters
500
A person’s weight on the moon is approximately one sixth of the weight on Earth. If a person’s weight on Earth is represented by the variable w, then the function that represents the weight on the moon in terms of the weight on Earth can be given as f(w) = 1/6 w. Find f^-1(30). Interpret the answer. Write your interpretation in a complete sentence.
180 If a person weighs 180 in Earth, then that person will weigh 30 on the moon.
500
Suzanne wants to invest $20,000 in an account for 25 years at an interest rate of 2.75% compounded continuously. Find the accumulated amount in the account at the end of 25 years.
20000e^(.0275*25)=39,775
500
Using the function: f(x)=(x^4-x^3+6)/x^2, find the oblique or non-linear asymptote.
y=x^2-x