Rational Functions
What's the domain of the function y=1/(x-1)?
All real numbers excluding x=1.
Is the expression 3x2-2x+√5 a polynomial?
Yes it is, you have only non-negative powers of the variable.
If f(x)=2x, find the value of f(4).
f(4)=16
What number is the base of the common logarithm (log)?
Base 10 (log(x)=log10(x))
What's the domain of the function f(x)=1/[(x+1)(x-2)]?
All real numbers excluding x=-1 and x=2.
Write the polynomial below in its standard form.
3x2-4x+x2-2x3+4x3+5
2x3+4x2-4x+5
Solve the equation 3x=81.
x=4
What's the name of the number "e" that is the base of the natural logarithm (ln)?
Euler's Number
How many vertical asymptotes does the function f(x)=(x+2)/(x2-4) have?
One vertical asymptote (and one removable discontinuity).
Factor the expression x2+3x.
x(x+3)
Solve the equation 2x+1=42
x=3
What's the value of the expression log464?
log464=3
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).
Factor the expression x2-2x-3.
(x-3)(x+1)
Simplify the expression (75)(7-1)/(49).
72 or 49
What's the value of the expression log93?
log93=1/2
Find the equation of the oblique asymptote of the function f(x)=(2x3 - x2 - 6x + 4)/(x2 - 3).
y=2x-1
Factor completely the expression x3+3x2-4x-12.
(x-2)(x+2)(x+3)
Simplify the expression (84)(1/4)2.
22 or 4
Solve the equation eln(6)=x
x=6