1 MAC1105, College Algebra Study Questions for Common Final ...

8. Here are the graphs asked for:
Y1 = x 3 y2 = x 2 y3 = 1/(x + 3) y4 = 1/x + 2
a. As x → + ∞: approaches + ∞, approaches + ∞,
approaches 0; approaches 2.
b. As x → −∞ : approaches −∞ , approaches +∞,
approaches 0, approaches 2.
9. a. ,,,
= ,,
= − 50,000; The African elephant population is decreasing by
an average of 50,000 elephants per year.
b. In 1980 the rate was twice as large as the rate computed in part (a) for 1930 to 2000. That
means that either before or after the 1980’s, the average rate of decline must have been much
smaller.
10.
X f(x) Average Rate of Change
0 0 n.a.
1 1 1
2 8 7
3 27 19
4 64 37
5 125 61
a. The function is increasing.
b. The average rate of change is also increasing.
11. a. Graph C b. Graph A c. Graph B
12. a. slope of segment A = [2 – (-6)]/[-4 – (-8)] = 8/4 = 2
slope of segment B = [-8 -2)/[0 – (-4)] = -10/4 = -2.5
slope of segment C = [-8 – (-8)]/[2-0] = 0/2 = 0
slope of segment D = [-6-(-8)]/[6-2] = 2/4 = 0.5
slope of segment E = [6-(-6)]/[10-6] = 12/4 = 3
slope of segment F = [-16 – 6]/[12 -10] = -22/2 = -11
b The slope of the segment F is steepest.
c. Segment C has a slope equal to 0.
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