Math 5 Trigonometry
fall ’06
Chapter 3 Test (2) Name____________________
Show all work for credit. Write all responses on separate paper.
1.
Compute and simplify the average rate of change of over the given interval. Remember that the average rate of change on
the interval [a, b] is the slope of the secant line connecting [a, f(a)] with [b, f(b)].
a. [0, 3]
b.
[a, a+h]
2. Find the maximum value of the given function and state its range in interval notation.
a.
b.
3.
Consider the quadratic
a. Express the quadratic function in standard form.
b. Sketch its graph.
c.
What transformations would be required to transform
this function to .
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4.
Given the graph of a.
b.
c.
d.
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5.
A mouse stands at point A on the bank of a straight canal, 20 feet wide. To reach point B,
70 feet down the canal on the opposite bank, it swims to a point P on the opposite bank and then crawls
the remaining distance to B. The mouse swims at 5 feet per minute and
crawls at 10 feet per minute.
6.
Consider
a.
Write a formula for the function that results from
shifting 2 units left, reflecting
in the y-axis and then stretching
horizontally by a factor 3, in that order.
b.
What transformations on f(x), in order, would
produce this formula:
7.
Suppose and
.
a.
Find the domain of
b.
Find the domain of
8.
Find a formula for the inverse function of and sketch a graph for
and
together showing the symmetry through the line
y = x.