Lesson 3 Quiz C
Name____________________________
1. The graph of y = f(x) is provided on the coordinate axes in each part of this task. On each
coordinate grid, sketch the graph that would result from the indicated transformation of f(x).
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a) g(x) = f(2x)
b) h(x) = 5f(x)
2. What function rule will produce functions related to the graph of f(x) = x3 in the following
ways?
a.
Horizontal stretch by a factor of 8 _______________________________
b.
Vertical compression by a factor of 6 _______________________________
c.
Reflection across the x-axis _______________________________
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3. The polynomial function p(x) has a local maximum at (–2, 6), a y-intercept of (0, 4), and
zeroes of –4 and 2.
a. Find the coordinates of the local maximum of the graph of g(x) = 8p(x). Explain your
reasoning.
b. What are the zeroes of h(x) = p(4x)? Explain your reasoning.
4. Find the transformation (x, y) →(?, ?) that maps the graph of f(x) onto the graph of g(x). Then
describe the transformation using words.
a. f(x) = cos x and g(x) = 12 cos 3x
b. f(x) = 5x3 – 7 and g(x) = 20x3 – 28
5. Suppose that the water depth at the end of a pier varies according to a function in the form
h(t) = a sin 0.4t + b, where t represents the number of hours since 8 A.M.
a. How many hours will there be between one low tide and the next low tide?
b. Suppose that the water depth at low tide is 2 feet and the water depth at high tide is 18 feet.
Find values of a and b so that the function h(t) = a sin 0.4t + b matches the situation.