Assignment
1) Consider the points (-7, - 6) and (3, 6).
(a) Determine the midpoint of the line segment with the given endpoints.
(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.
2) Consider the following graph and determine a), b), c) and d):
(a) State the x-intercept(s)
(b) State the y-intercept(s).
(c) State the domain.
(d) State the range.
3) Consider the following function:
f(x) = (x - 6)/(x- 4)
(a) Calculate f(-3).
(b) State the domain of the function f(x), written in interval notation.
(c) Compute f(a-1) and simplify as much as possible.
4) Let y = 8 - 2x2.
(a) Find the y-intercept(s) of the graph of the equation, if any exist.
(b) Find the x-intercept(s) of the graph of the equation, if any exist.
(c) Create a table of sample points on the graph of the equation (include at least five points), and use them to help 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.)
(d) 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.
(e) 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.
(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.
5) (See textbook page 82 for definitions of the economic functions used in this problem.)
The cost, in dollars, for a company to produce xmotor part is given by C(x) = 1400 + 7x for x ≥ 0, and the price-demand function, in dollars per widget, is p(x) = 16 - 0.01x for 0 ≤ x ≤ 1600.
(a) Find and interpret C(400).
(b) Find and interpret C ¯(400). (Note that C ¯(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(400), where P(x) is the profit function in part (d).
6) Let f (x) = 7x2 - 5x + 6 and g(x) = 3 - 5x.
(a) Find the difference function (f - g)(x) and simplify the results. .
(b) Find (g - f)(-1).
(c) Find (f ·g)( -1). (That is, the product function of "f" times "g", evaluated at x = -1).
7) For income x (in dollars), the state's income tax T (in dollars) is given by
T(x)={(0.02x&if 0 ≤x≤2,000@40+0.03(x-2000)&if 2,0004,000)¦
(a) What is the tax on an income of $3,800?
(b) What is the tax on an income of $56,000?
8) f is a function that takes a real number x and performs these three steps in the order given:
a) Take the square root.
b) Subtract 2 from the result.
c) Take the reciprocal of the result.
(That is, make the quantity the denominator of a fraction with numerator 1.)
d) Find an expression for f (x). (no explanation required)
9) Given f(x)=x-3 and g(x)=√(x-1), which of the following is the domain of the quotient function ?
A. (1,∞)
B. [+ 1,∞) ¦
C. [+ 1,3) ¦ ∪ (3,∞)
D. (-∞,3)∪(3,∞)
10) Let f(x) = (x - 3)/(x^2- 7x )
(a) Calculate f(2). (work optional)
(b) State the domain of the function f(x) = (x - 3)/(x^2- 7x )
(c) Find f(3a) and simplify as much as possible. Show work.