Solve the inequality.
(x+2)/(x-4) >= 0
(>= means greater than or equal to)
(9)
x > 4 or x <= -2
100
Show f(g(x)) = x and g(f(x)) = x for
f(x) = 2x3 + 1 and
g(x) = cbrt((x-1)/2)
(3)
Check work...
100
Simplify:
sqrt(8)/(21/2)
(15)
2
100
Are you going to have to graph things on this test?
Yes
100
What is the period of the sine and cosine functions, and why?
The period is 2pi. After 2pi values begin to repeat as you begin another trip around the unit circle.
200
Find the domain.
f(x) = sqrt(x2-x-6)/(x-5)
(45)
x <= -2 , 3 <= x < 5 , 5 < x
200
Is this function one-to-one?
f(x) = x4+2
(9)
Yes, it is one-to-one.
200
What is x in simplest form?
4lnx = -8
(31)
e-2
200
Which of the following shifts f(x) c units to the left (c > 0)?
A. f(x)+c
B. f(x)-c
C. f(x+c)
D. f(x-c)
(0)
C. f(x+c)
200
Find all possible x between 0 and 2pi:
sin2x-4sinx+3=0
(9)
x = pi/2
300
Find all the zeros.
f(x) = x2-4x+2
(67)
x = 2 +/- sqrt(2)
300
If f(x) = x3+4x-1,
find f-1(-1)
(13)
0
300
Simplify:
log3(1/27)
(37)
-3
300
Find f(g(x)) and g(f(x)) for f(x) = x2+1 and g(x) = sinx.
(5)
f(g(x)) = sin2x+1
g(f(x)) = sin(x2+1)
300
Given that the answer is between pi and 3pi/2, simplify:
tan-11
5pi/4
400
Find all the vertical asymptotes.
f(x) = (x2+1)/(x3+3x2+2x)
(21)
x = 0, x = -1, x = -2
400
Explain why this statement is true:
If the graph of f does not intersect the line y = 3, then f-1(x) is undefined at x = 3.
(25)
If the original function doesn't take the value of 3 for any x, then 3 is not in the domain of the inverse function. There would be nothing to map it back to.
400
Rewrite as a single logarithm in the simplest possible form:
ln(3/4) + 4ln2
(45)
ln(12)
400
Find functions f(x), g(x), and h(x) such that f(g(h(x))) is equal to
cos3(4x-2)
(19)
h(x) = 4x-2, g(x) = cosx, f(x) = x3
400
Prove that 1 + cot2x = csc2x.
Divide sin2x + cos2x = 1 by sin2x.
500
Using a calculator, find all the extrema of
f(x) = 3x/(sqrt(x2+4))
(15)
There aren't any.
500
What symmetry does the graph of a function and its inverse always have?
(0)
Reflection symmetry across the line y = x.
500
What is the inverse function of f(x) = ex ?
(0)
f-1(x)=lnx
500
Where does g(x) = -3(x2-1)+2 move the graph of f(x) = x2-1 to?
(47)
Reflects over x-axis, vertical stretch by factor of 3, vertical shift 2 up