Download Practice Exam for Exam 2

Math 101
Hour Exam II
Name__________________________________________
1. Find the linear equation:
a) joining the points (4, −2) and (3, 5).
b) determined by the function values f(5) = 1 and f(7) = 0.
2. A cable television company charges a $85 installation fee and $70 per month for
service. Write an equation for the total cost for t months of service and calculate the
cost of a full year of service.
3. Find the relative maximum and/or minimum of the function G(x) = 4x − 4x 3 and
the interval(s) on which G(x) is increasing, decreasing, or constant.
Maximum______________________
Minimum_______________________
G(x) is increasing on the interval(s)_______________________________
G(x) is decreasing on the interval(s)_______________________________
G(x) is constant on the interval(s)_________________________________
3. Let f(x) = x 2 – 4 and g(x) =
x
. Find and simplify:
2x + 6
a) (f – g)(−2)
b) (f ∘ g)(0)
c) (g ∘ f)(x)
d) The domain of g(x) in interval notation
e) The domain of f(x) in interval notation
4. Simplify the difference quotient
f (x + h ) − f (x )
when f(x) = x 2 + 2.
h
5.
Find the equation of a function which resembles y =
1
shifted right 3 units and
x
down 7 units.
6.
Sketch a graph of the function f(x) = 4x − 6, x ≤ 3
3 − x, x > 3
Label at least 3 points.
7. Use algebra to determine if the graph of the function y =
4x
shows symmetry to
1− x
the x-axis, the y-axis, the origin, or none of these.
8. Find the equation of a line passing through (3, −2) which is parallel to the line
2x − 6y = 1.