College Algebra

Exponents

100

(x²)(x⁵)

What is x⁷?

200

(x²)³

What is x⁶ ?

300

b⁶/b⁹ Express your answer without negative exponents.

What is 1/b³ ?

400

(2x²y⁶)³

What is 8x⁶y¹⁸?

Periodic Functions

100

The equation of the midline of the function f(x)=3sin(4x)-5

What is y=-5?

200

The period of the cosine function f(x)=3cos(2x)+4

What is 180 degrees?

300

The range of the function f(x)=4cos(8x)-2

What is [-6, 2] ?

400

Find the equation of a sine function with an amplitude of 5, a period of 90 degrees, and a midline of y = 1.

What is f(x)=5sin(4x)+1?

Equations

100

x²+5x-36=0

What are x = -9 and x = 4 ?

200

Find the solutions of the equation f(x)=4x²-13x+3=0.

What are x = 1/4 and x = 3 ?

300

Solve the system of equations 5x-4y=9 and x - 2y =-3

What is x =5 and y = 4?

400

Find the solutions of x²+4x-7=0.

What are -2 +/- sqrt(11) ?

Exp & Logarithms

100

log10⁵

What is 5?

200

Completely expand the logarithmic expression log(x²y⁴).

What 2log(x)+4log(y)?

300

Solve the exponential equation 4^x=15. Express your answer as a decimal.

What is 1.953 ?

400

Solve the logarithmic equation log(x+4)-log(x-5)=1.

What is x = 6 ?

Functions

100

f(-2) if f(x)=-x²+5x

What is -14?

200

f(g(2)) if f(x)=x²-3x and g(x)=4x-2.

What is 18?

300

For the functions f(x)=x²+2x and g(x)=3x-1, find g(f(x)) and completely simplify the result.

What is 3x²+6x-1?

400

For the functions f(x)=x²+2x and g(x)=3x-1, find f(g(x)) and completely simplify the result.

What is 9x²-1?