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Mathematics 141 test two
Wednesday, June 3, 2009
please show your work to get full credit for each problem
1. Use a calculator to estimate the values of
(a) e.04x when x = 30
(b) log2 1912
2. Is y a one-to-one function of x ?
3. Is y a one-to-one function of x ?
y
x y
2 0
3 5
5 9
6 0
x
4. Rewrite as a logarithmic equation:
5. Rewrite as an exponential equation:
ep = M
log16 N = y
6. What is the inverse function of g(x) = log x ?
7. Simplify:
(assume that b > 0)
(b) logb b4
(a) logb 1
(c) 10log x
(d)
8. If logb 3 = 0.56 and logb 4 = .71 find values for
(a) logb 4/3
(b) logb 3100
9. Solve for x:
(c) logb 12
10. Solve for H:
1.0512x = 2
ln x = 2.6
b3 (b5 )2
b−4
page two
11. For the functions f (x) = 2x2 and g(x) = 4x3 −3x, compute a formula for the composition
function g(f (x)).
√
12. For the function H(x) = x + 5, write down formulas for the functions f and g which
compose to H, in other words, H(x) = f (g(x)).
13. For the polynomial f (x) = −2x(x + 80)3 (x − 5)2
(a) state the degree of the polynomial
(b) list each real zero and its multiplicity
(c) sketch a graph of this polynomial. Your graph should should the correct x-intercepts, the
correct shape of the graph for large values of |x|, and the correct shape near the x-intercepts.
14. For the polynomial g(x) = x3 + 8x2 + 22x + 20,
(a) what is the total number of real & complex zeroes this polynomial will have ?
(b) one solution of this polynomial is x = −2. Use this information, long or synthetic
division, and the quadratic formula to find the other solutions (which are complex numbers ! )
15. Use logarithm properties to expand:
16. For the the rational function G(x) =
10(x − 2)3
√
log
w
!
10x + 4
3x + 8
(a) what is the domain of the function?
(b) write equations for any vertical, horizontal, or oblique asymptotes of the function.
(c) Sketch a graph of the rational function. Your graph should show the exact locations of
all asymptotes, intercepts, and the graph’s correct shape.
17. For the logarithmic function f (x) = log3 (x + 4)
(a) state the domain of the function
(b) sketch a graph which shows the correct shape, and includes any asymptotes & intercepts.