College Algebra Review

Just the Basics

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

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)

300

Answer using the function: f(x) = -3 + √(x+4) state the domain state the range

domain: [-4, infinity) range: [-3, infinity]

400

Solve the following absolute value equation: 2|x-4|+3=9.

x= 1, 7

500

Solve the absolute value inequality: 5+2|2x-4|≥11. Write your answer in interval notation.

(-infinity, 1/2] U [7/2, infinity)

Perfect Parabolas

100

Use the function, f(x) = x^2 – 2x -15 to answer the following: Determine the concavity of f(x).

concave up

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

300

(5+3i)(3-4i)

27-11i

400

Solve the quadratic inequality: -2x^2-13x+24≥0. State your answer in interval notation.

[-8, 1.5]

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

What's the Inverse?

100

Find the inverse if f(x)= (2x-3)/4

f^-1(x)=(4x+3)/2

200

Given f(x) = 2x^2-x-4 and g(x) = x+6: Find ( f/g ) (-2).

3/2

300

Given f(x) = 2x^2-x-4 and g(x) = x+6: Find (g o f)(x).

2x^2-x+2

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

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.

Extra Special Logs

100

Evaluate the logarithm: log5 1

0

200

Solve for x: 2 = 12 – 2 ln(8.1x)

x=(e^5)/8.1 = 18.32

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)

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

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

What's an asymptote?

100

Given the function, f(x)=(x+1)〖(x-2)〗^2 (x+3) State the degree

4

200

Given the function, f(x)=(x+1)〖(x-2)〗^2 (x+3): State the end behavior

both ends go up

300

Given the rational function, f(x) = (x^2-x-6)/(x^2-9), find the vertical asymptotes

x=-3

400

Given the rational function, f(x) = (x^2-x-6)/(x^2-9), find the horizontal asymptote.

y=1

500

Using the function: f(x)=(x^4-x^3+6)/x^2, find the oblique or non-linear asymptote.

y=x^2-x