Math 1300 Written Homework #10 Solutions 4.2, Q. 24. Let y = at 2e ...

4.3, Q. 50. Consider the family
y = A
x + B .
a. If B = 0, what is the effect of varying A on the graph?
Solution: We have the family y = A
. Varying A corresponds to rescaling the y-values
x
of the graph, so increasing A will stretch the graph vertically. It will still have the same
basic shape (vertical asymptote at x = 0, horizontal asymptote at y = 0).
b. If A = 1, what is the effect of varying B?
Solution: We have the family y = 1
, which has a vertical asymptote at x = −B.
x + B
Varying B moves this vertical asymptote, but does not change the shape of the graph.
c. On one set of axes, graph the function for several values of A and B.
Solution: Here I have graphed: A = 1, B = 1 in red, A = 2, B = 1 in blue, A = 1,
B = −2 in yellow, and A = −1, B = −2 in green.
4.3, Q. 54. For positive A, B, the force between two atoms is a function of the distance, r, between them:
f(r) = − A B
+
r2 r3 r > 0
a. What are the zeros and asymptotes of f?
Solution: It’s easier to answer this by getting a common denominator:
f(r) =
B − Ar
r3 .
This is zero when r = B/A, and it has a vertical asymptote when r = 0. It has a
horizontal asymptote at y = 0.
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