1. Given the following quadratic equation, **Y=x^2+6x+5, **find

a. the vertex

b. the axis of symmetry

c. the intercepts

d. the domain

e. the range

f. the interval where the function is increasing, and

g. the interval where the function is decreasing

h. Graph the function.

SHOW ALL WORK.

2. Given the following polynomial, **f(x)=(x+5)(x-3)(x+3),**find

a. the zeros and the multiplicity of each

b. where the graph crosses or touches the x‐axis

c. number of turning points

d. end behavior

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3. Using the 7 steps outlined in Section 4.3 of your book, analyze the graph of the following function:

R(x) = x+1/x

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4. Solve the following inequality. Write your solution in interval notation.

X^3 + 81x > 0

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5. Find the domain of the composite function* f* °*g*

F(x) = x^2 + 5 ; g(x) = √x-8

6. Find the inverse of the following function. Find the domain, range, and asymptotes of each function.

Graph both functions on the same coordinate plane.

F(x) = 12e^-x