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Math 1147 Exam #1

HONOR CODE: On my honor, I have neither given nor received any aid on this
examination.

Signature :

Instructions: Do all scratch work on the test itself. Make sure your final answers
are clearly labelled. Be sure to simplify all answers whenever possible. SHOW
ALL WORK ON THIS EXAM IN ORDER TO RECEIVE FULL CREDIT!!!

No. Score
Bonus /10
total /100

1. (a) Determine whether the relation represents a function.
Justify your answer. If it is a function, state the domain
and range.

You will be given the relation as a diagram with arrows
between the two sets . From section 3.1.

(b) Determine whether the relation represents a function.
Justify your answer. If it is a function, state the domain
and range.

You will be given the relation as ordered pairs. From section
3.1.

(c) Determine whether the the equation defines y as a function
of x.

Justify your answer.
You will be given the relation as an equation. From section
3.1.

2. Let f(x) be the piecewise defined function

You will be given a piecewise-defined function.
From section 3.4.

(a) Find f(You will be given some number).
(b) Find f(You will be given some number).
(c) Find the domain of f(x).
(d) Sketch the graph of f (x).

3. Graph the function.
You will be given a function and will need to graph it using
transformations. From section 3.5.

4. Graph the function.
You will be given a function and will need to graph it using
transformations. From section 3.5.

5. Determine the function whose graph is given.
You will be given the graph and asked to determine what the
function is. From section 4.3.

6. Graph the given polynomial function .
You will be given a polynomial function in factored form . From
section 5.1.

7. Graph the given rational function .
You will be given a rational function in factored form. From
section 5.3.

8. Solve each inequality .
(a) You will be given a polynomial inequality. From section 5.4.
(b) You will be given a rational inequality. From section 5.4.

9. Let f(x) be given below. Find the following.

f(x) = You will be given a function. From section 5.5

(a) The maximum number of real roots of f.
(b) The number of possible positive and negative zeros of f.
(c) All the possible rational zeros of f .

10. Let f(x) be the polynomial function below. Find all the real
zeros of f(x) and use them to factor f over the reals.

f(x) = You will be given a function and will need to find the zeros
and factor it. From section 5.5.

11. Let f(x) be the quadratic function given below. Answer the
following questions about f(x).
Be sure to justify all your answers.

f(x) = You will be given a quadratic function. From section 4.3.

(a) Does the graph of f open up or down? How do you know?
(b) What is the vertex (h; k) of f?
(c) What are the intercepts of f ?
(d) What is the domain of f?
(e) What is the range of f?
(f) What are the intervals of increase and decrease of f?
(g) What does the graph of f look like ?

12. Let f(x) be the polynomial function given below. Use the given
zero to find the remaining zeros. Then use that to write f in
factored form.

f(x) = You will be given a function and at least one complex zero .
From section 5.6.

Bonus. This will be some problem which somehow involves needing
to find the zeros of a polynomial function, such as finding
the x-intercepts of a polynomial function as in section 5.1
or finding the domain or vertical asymptotes of a rational
function, as in section 5.2/5.3 or solving a polynomial or
rational inequality, as in section 5.4. But the difference with
this one is that the polynomial
will be more complicated than
in the sections where they were in the book, so solving the
problem will require using the material from section 5.5.

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