Exponents and Radicals

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)