Homework Assignment

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MATH 107

• Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document containing your work. Scanned work is also acceptable. In your document, be sure to include your name and the assertion of independence of work.

1) Graphs for two functions f(x) and g(x) are given below. Formulas for them are not given. Determine the following. (10pts)

a) Estimate the equation of function f(x). Show your work.

b) Estimate the equation of function g(x). Show your work.

c) Find the coordinates of the intersection point of the two functions f(x) and g(x) and show your work.

d) How are the two lines represented by functions f and g relate to one another?

(Hint: parallel, perpendicular, neither). Prove your answer numerically.

2) Consider the following graph of a function y = f(x). (Assume that the domain is all real numbers and the graph continues beyond the graph window.) (8 pts)

a) Referring to the graph, on what interval(s) is the function f increasing?

y=f(x)

A. (– ∞, – 6) ∪ (–4, 0) ∪ (3, ∞)

B. (– ∞, –6) ∪ (-4, 0)

C. (– ∞, – 4) ∪ (–4, 3) ∪ (3, ∞)

D. (–4, 3)

b) Referring to the graph, what is true about the graph’s symmetry?

(Hint: Dashed vertical line crosses x axis at x = -4 and x= 3)

A. symmetric with respect to the x-axis

B. symmetric with respect to the y-axis

C. not symmetric

D. symmetric with respect to the x-axis, the y-axis, and the origin

3) The table below shows the comparison of the cost, in dollars, of a $100,000 life insurance policy for female non-smokers at certain ages.

Model the data with a linear function using age 32 and 35. Then predict the cost of life insurance for a female non-smoker of age 40. Round to the nearest dollar. (8 pts)

4) Consider the following graph of a function y = f(x). (Assume that the domain is all

real numbers and the graph continue beyond the graph window.) (8 pts)

a) Referring to the graph, on what interval(s) is the function f increasing?

y= f(x)

A. (– ∞, – 6] ∪ (–4, 0) ∪ [3, ∞)

B. (– ∞, –4) ∪ (3, ∞)

C. (– ∞, – 4) ∪ (–4, 3) ∪ (3, ∞)

D. The function is not increasing

b) Referring to the graph, what is true about the graph’s symmetry?
(Hint: Dashed vertical line crosses x axis at x = -4 and x= 3)
A. symmetric with respect to the x-axis
B. symmetric with respect to the y-axis
C. not symmetric
D. symmetric with respect to the x-axis, the y-axis, and the origin

5) Consider the following graph of a function y = f(x). (8 pts)

(Assume that domain of the function is [-4, 6]

Referring to the graph, on what interval(s) is the function f decreasing?

A. [– 4, -2] ∪ [3, 4] ∪ [5, 6]

B. (– 2, 3) ∪ (4, 5)

C. (– 2, 3)

D. [5,6]

6) The table below shows the average number of lunches per day, sold for various years.

Model the data with a linear function using years 1 and 3 and estimate the average number of lunches sold per day in 2013 using this function. Round to the nearest whole number of lunches. (8 pts)

7) The graph of the function f is shown below. (8pts)

Which of the following represents the graph of g(x) = -f(x) + 2?

8) Graph the following function: (14 pts)

9) Given the following functions. (8 pts)

a) Find (f – g)(-2) = ?

b) Find (fog)(-2) = ?

10) Perform the division and simplify. (6 pts)

11) Simplify. (6 pts)

=

12) Which one of the graphs belongs to the given function: (8 pts)