Homework Assignment 11 (25 points)
You must show work to get credit. Partial credit is available for correct steps toward the
answer. No outside assistance. Get help on different, related problems.
0. (5 points) Correct submission format, and not submitted super late.
Section 5.1
Instructions for 1-3:
Sketch the graph of the function and determine whether it is one-to-one, and
demonstrate how you used the horizontal line test.
(3 points each)
1. f (x)=√100−x2
2. r(x)=400−20x
3. k(x)=−x2−4x+10 ,x≥0 (Hint: Remember that the vertex
is at -b/2a. You could graph the whole parabola to get an idea, but remember to delete the part
outside of the specified domain.)
Section 5.2
Instructions for 4-5
In the book, a basic exponential function f has the form f (x)=ax for some
a>0 ,a≠1 . We’re going to look at a few functions which are transformations of basic
exponential functions. For example, g(t)=100⋅2t−2+60 is built from the basic exponential
function b(t)=2t .
a. Specify the basic exponential function from which the function is built. Graph
the basic exponential function. Include the horizontal asymptote, where the output variable is
0.
b. Use transformations to graph the function itself. Include the new horizontal
asymptote.
(3 points each, instructions above)
4. A(t)=5000e0.05t
5. g(x)=81⋅(
2
3
)
t
Section 5.3
6. (3 points) Graph f (x)=2x and f−1(x)=log2(x) on the same
axes. Label the two functions, include the axis of reflection y=x , and include the asymptotes.
Include at least three points from the from the graph of f .
7. (2 points) Use the change of base formula and one of the two
standard logarithms (base 10 or base e) to compute the value. You must show what you entered
into the calculator:
log1.005(2)
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