Fundamentals
Evaluate
5^23/5^21
25
Find the domain of
1+ sqrt(x)
[0,infty)
Find g(f(-2))
f(x) = 2x-3
g(x)=4-x^2
-45
Combine the polynomial.
P(x)=-(x-1)^2(x+2)^2
P(x)=-x^4 - 2x^3 + 3x^2 + 4x - 4
Evaluate the expression without a calculator.
log25+log4
2
Factor
2x^2-5x-12
(2x+3)(x-4)
Find the average rate of change of f(x) between x=1 and x=4
f(x)=(x+2)^2
The average rate of change is 9.
Find g o f
f(x) = 2x-3
g(x)=4-x^2
g o f = -4x^2 + 12x - 5
What is the national animal of Scotland?
Unicorn
Expand the logarithmic expression.
lnsqrt((x^2-1)/(x^2+1)
1/2[ln(x+1)+ln(x-1)-ln(x^2+1)]
Find all the real solutions of the equation
x^4-3x^2+2=0
+-1, +-sqrt(2)
Write down the vertex form.
f(x) = a(x-h)^2 + k
Find all extraneous solutions
g(x)= (1/x-1) - 3 = (x/ (x-1))
x = -2
Find the domain in interval notation.
(x^2-5x+6)/(x^2-4)
(-infinity, -2) U (-2, 2) U (2, infinity)
Solve the equation.
3^(2x-7)=27
x=5
Simplify
((3x^(3/2)y^3)/(x^2y^(-1/2)))^(-2)
x/(9y^7)
Suppose the graph of f is given. Describe how the graph of the following function can be obtained from the graph of f.
y=-f(x-2)-2
Function f is reflected over the x-axis, shifted right 2 units, and shifted down 2 units.
Find f(g(x))
f(x) = x^2-3x+2
g(x)=4-3x
9x^2-15x+6
What is the domain of r(x)?
r(x)=(x^2+5x-14)/(x-2)
D: (-infty, 2)cup(2,infty)
Combine into a single logarithm.
log(x-2)+log(x+2)-1/2log(x^2+4)
log((x^2-4)/(sqrt(x^2+4)))
Describe the trigonometric ratios of Sin, Cos, and Tan.
Sin = o/h
Cos = a/h
Tan = o/a
Determine whether f is even, odd, or neither.
f(x)=2x^5-3x^2+2
Neither
Find the inverse function of
f(x)=(x-3)/(2x+5)
f^-1 (x)= - (5x+3)/(2x-1)
Find the x-intercept, y-intercept, and domain of the rational function r(x).
r(x)=(x^2+3x-18)/(x^2-8x+15)
x-intercept: (-6, 0)
y-intercept: (0, -6/5)
D: (-infty, 3)cup(3,5)cup(5,infty)
Solve the equation.
log_3(x-8)+log_3x=2
x=9