Math 1090
Midterm 2 Review
1. Solve for x
1
1
2
−
=
x−5 x+1
4
2. Suppose logb x = 32 , logb y = 5, and logb z = −4. Compute
4√ x z
logb
y
1
3. Consider the function h(x) = |4(x − 1)| + 2.
(a) What is the base function, f (x), for h?
(b) Describe each transformation f has undergone to become h.
(c) Write h as a transformation of f .
(d) Graph f and h on the axes.
10
y
K10
5
K5
0
5
x
K5
K10
2
10
4. Let p(w) =
3w
.
4w+9
Find p−1 (w).
5. Simplify the following expression completely:
√
3
x2 85/6
q .
1/2
8 3 x1
3
6. Consider the polynomial function y = 19 (x2 − x − 6)2 .
(a) What is the degree of y?
(b) What is the y-intercept?
(c) Find all the roots of y.
(d) Sketch the graph of y on the axes provided.
10
y
K10
5
K5
0
5
x
K5
K10
4
10
7. If g(p) =
p
p2 − 4, evaluate g(w2 + 1).
8. Solve each equation.
(a)
ln 5 + ln x = ln(3x + 10).
(b)
2x10x = x2 10x
5