Please see the attachment. Show all work and all steps and answer the question fully

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Show work/explanation where indicated. Answers without any work may earn little, if any, credit.

1. (4 pts)

Which of these graphs of relations describe y as a function of x?

That is, which are graphs of functions?

Answer(s): ____________

(no explanation required.) (There may be more than one graph which represents a function.)

2. (10 pts)

Consider the points (–5, –6) and (–1, 10).

(a) State the midpoint of the line segment with the given endpoints. (No work required)

(b) If the point you found in (a) is the center of a circle, and the other two points are points on the

circle, find the length of the radius of the circle. (That is, find the distance between the center

point and a point on the circle.) Find the exact answer and simplify as much as possible. Show

work.

3. (12 pts) Consider the following graph of y = f (x).

(no

explanations

required)

(a) State

the xintercept(s)

.

(b) State

the yintercept(s)

.

(c) State

the

domain.

(d) State

the range.

3. (8 pts)

Let 𝑓(𝑥) =

𝑥+ 5

(𝑥− 4)2

(a) Calculate 𝑓(−2). (work optional)

(b) State the domain of the function 𝑓(𝑥) =

𝑥+ 5

(𝑥− 4)2

(c) Find 𝑓(𝑎 + 7) and simplify as much as possible. Show work.

4. (7 pts)

f is a function that takes a real number x and performs these four steps in the order given:

(1) Multiply by 2.

(2) Add 1.

(3) Take the square of the whole quantity.

(4) Take the reciprocal. (That is, make the quantity the denominator of a fraction with numerator 1.)

(a) Find an expression for f (x). (no explanation required)

(b) State the domain of f. (no explanation required)

5. (6 pts)

Given 𝑓(𝑥) = 𝑥 − 2 and 𝑔(𝑥) = |𝑥 + 5|, which of the following is the domain of the

quotient function f / g ?

A. (−5, ∞)

B. (−∞, −5) ∪ (−5, ∞)

C. (−5, 2) ∪ (2, ∞)

D. (−∞, −5) ∪ (−2, ∞)

Explain.

6._______

6. (6 pts)

For income x (in dollars), a particular state’s income tax T (in dollars) is given by

0.028𝑥

𝑖𝑓 0 ≤ 𝑥 ≤ 3000

𝑇(𝑥) = { 70 + 0.035(𝑥 − 2500) 𝑖𝑓 3000 < 𝑥 ≤ 8000
245 + 0.050(𝑥 − 7,500)
𝑖𝑓 𝑥 > 8000

(a) What is the tax on an income of $53,000? Show some work

(b). What is the tax on an income of $5,300? Show some work.

7. (20 pts)

Let y =1 − 2×2.

(a) Find the x-intercept(s) of the graph of the equation, if any exist. (work optional)

(b) Find the y-intercept(s) of the graph of the equation, if any exist. (work optional)

(c) Create a table of sample points on the graph of the equation (include at least six points) and create a

graph of the equation. (You may use the grid shown below, hand-draw and scan, or you may use the free

Desmos graphing calculator described under Course Resource to generate a graph, save as a jpg and

attach.)

x

y

(x, y)

(d) Is the graph symmetric with respect to the y-axis? _____ (yes or no). If no, state a point on the

graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the

textbook.

(e) Is the graph symmetric with respect to the x-axis? _____ (yes or no). If no, state a point on the

graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the

textbook.

(f) Is the graph symmetric with respect to the origin? _____ (yes or no). If no, state a point on the

graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the

textbook.

8. (12 pts)

Let f (x) = 3×2 + 4x – 8 and g(x) = 3 – 2x.

(a) Evaluate the function g – f for x = –2. That is, find (g – f)(–2). Show work.

(b) Evaluate the function fg for x = –2. That is, find (f g)( –2). Show work.

(c) Find the difference function (f – g)(x) and simplify the results. Show work.

9. (15 pts)

(See textbook page 82 for definitions of the economic functions used in this problem.)

The cost, in dollars, for a company to produce x widgets is given by C(x) = 4150 + 7.00x

for x 0, and the price-demand function, in dollars per widget, is p(x) = 45 − 0.03x for 0

x 2250.

(a) Find and interpret C(300).

(b) Find and interpret 𝐶̅ (300). (Note that 𝐶̅ (x) is the average cost function.)

(c) Find and simplify the expression for the revenue function R(x). (work optional)

(d) Find and simplify the expression for the profit function P(x). (work optional) Note that

p(x) and P(x) are different functions.

(e) Find and interpret P(300), where P(x) is the profit function in part (d).