Algebra II - Jeopardy

Rational Functions

100

What's the domain of the function y=1/(x-1)?

All real numbers excluding x=1.

200

What's the domain of the function f(x)=1/[(x+1)(x-2)]?

All real numbers excluding x=-1 and x=2.

300

How many vertical asymptotes does the function f(x)=(x+2)/(x²-4) have?

One vertical asymptote (and one removable discontinuity).

400

How many vertical asymptotes does the function f(x)=1/(x²+4)?

No vertical asymptotes, because the denominator is never equal to zero (when x is a real number).

500

Find the equation of the oblique asymptote of the function f(x)=(2x³ - x² - 6x + 4)/(x² - 3).

y=2x-1

Polynomials

100

Is the expression 3x²-2x+√5 a polynomial?

Yes it is, you have only non-negative powers of the variable.

200

Write the polynomial below in its standard form.

3x²-4x+x²-2x³+4x³+5

2x³+4x²-4x+5

300

Factor the expression x²+3x.

x(x+3)

400

Factor the expression x²-2x-3.

(x-3)(x+1)

500

Factor completely the expression x³+3x²-4x-12.

(x-2)(x+2)(x+3)

Exponentials

100

If f(x)=2^x, find the value of f(4).

f(4)=16

200

Solve the equation 3^x=81.

x=4

300

Solve the equation 2^x+1=4²

x=3

400

Simplify the expression (7⁵)(7^-1)/(49).

7² or 49

500

Simplify the expression (8⁴)(1/4)².

2² or 4

Logarithms

100

What number is the base of the common logarithm (log)?

Base 10 (log(x)=log₁₀(x))

200

What's the name of the number "e" that is the base of the natural logarithm (ln)? 

Euler's Number

300

What's the value of the expression log₄64?

log₄64=3

400

What's the value of the expression log₉3?

log₉3=1/2

500

Solve the equation e^ln(6)=x

x=6