Math Worksheet

MATH 165 — Group Homework Assignment 1

Neatly write the name and section number of each group member who worked on this assignment. Each submission can have at most five people. Indicate with a (∗) the person to whom the graded assignment should be returned.

This assignment must be submitted by Friday, September 7 by 4 pm. No late work will be accepted. The assignment may be submitted during recitation or in Carver 396.

Last name, First name Section Last name, First name Section

Last name, First name Section Last name, First name Section

Last name, First name Section

For this assignment your group will create a function G(x) which has the following properties:

(i) The domain of G(x) is −5 ≤ x < 5 and |G(x)| ≤ 7 for all x. (ii) G(x) is continuous at all points in the domain except at x = −1 and x = 2.

(iii) The average rate of change of G(x) between x = −4 and x = −2 is −3. (iv) G(x) is not a single line segment for −4 ≤ x ≤ 2. (v) The slope of the tangent line to G(x) at x = 4 is 2.

(vi) lim x→−1−

G(x) = 2 and lim x→−1+

G(x) = 4 and G(−1) = 1.

(vii) lim x→2

G(x) = −1 and G(2) = −3.

The following must be completed to receive full credit:

1. Give a “formula” for a function G(x) that satisfies these properties. (Consider using a piece-wise defined function.)

2. Give a written justification that the slope of the tangent line to G(x) at x = 4 is 2 using the function given in item (1). Make sure to include an explanation of your justification; computations without any additional explanation will not receive full credit.

3. Graph the function G(x) on the axes provided.

There are many possible answers and each group should find their own solution.

1 2 3 4 5−2−3−4−5

7

6

5

4

3

2

1

−1

−2

−3

−4

−5

−6

−7

−1 x

y