Define a function with independent variable

Question

Complete the below:

1. Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y.
x|y| = x + 9

2. Use the graph of the function to estimate:

a. f(2)
b. f(-4)
c. All x such that f(x) = 0

3. For the following graph:

a. Find the domain of f.

b. Find the range of f.
c. Find the x-intercepts.
d. Find the y-intercept.
e. Find the intervals over which f is increasing.
f. Find the intervals over which f is decreasing.
g. Find the intervals over which f is constant.
h. Find any points of discontinuity.

4. Use the following to answer questions a-d:

f(x) = x2 + x and g(x) = x - 5

a. Find h(x) = (f ? g)(x).
b. State the domain of h(x) = (f ? g)(x).
c. Find h(x) = (g ? f)(x).
d. State the domain of h(x) = (g ? f)(x).

5. The graph of the polynomial function P(x) is shown.

a. List the real zeros of P(x).
b. List the turning points of P(x).
c. State the left and right behavior of P(x).

6. $2,350 is invested in account paying 9% compounded semiannually. How much will the account be worth after 8 years? Show your work.

7. Change each exponential form to an equivalent logarithmic form:

a. 32 = 2⁵
b. 1/125 = 25^-3/2
c. 12 = 144^1/2

8. Change each logarithmic form to an equivalent exponential form:

a. log₃81 = 4
b. log ₁₀0.0001 = -4
c. log₃(1/243)=-5