Page 41 - Calculus Workbook For Dummies

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Chapter 2: Funky Functions and Tricky Trig

Solutions to Functions and Trigonometry

a Which of the four relations in the figure represent functions and why? A and D.
The circle and the S-shaped curve are not functions because they fail the vertical line test: You
can draw a vertical line somewhere on their graphs that touches the curve more than once.
These two curves also fail the algebraic test: A curve is a function if for each input value (x)
there is at most one output value (y). The circle and the S-shaped curve have some xs that cor-
respond to more than one y so they are not functions. Note that the reverse is not true: You can
have a function where there are two or more input values (xs) for a single output value (y).
b If the slope of line l is 3,
a. What’s the slope of a line parallel to l? The answer is 3.
1
b. What’s the slope of a line perpendicular to l? The answer is - , the opposite reciprocal of 3.
3
x
c Sketch a graph of f x = e .
^ h
y
f(x) = e x
6
5
4
3
2
1
x
-3 -2 -1 1 2 3 4 5 6
-1
-2
-3

d Sketch a graph of g x = lnx.
^ h

y
6
5
4
3 g(x) = lnx
2
1
x
-3 -2 -1 1 2 3 4 5 6
-1
-2
-3