Module 08 – Homework 08

From 3.4

1.Given .

(a) Find the -intercepts of .

(b) Find .

(c) Use test points within the intervals formed by the -intercepts to determine the sign of in the interval.

(d) Graph.

2. Use the intermediate value theorem to determine,if possible, whether the function has a real zero between the numbers given.

(a); -5 and -4

(b); -3 and -2.

3.Use the boundedness theorem to show that has no real zero less than -3 and no real zero greater than 3.

4. Given , approximate each real zero as a decimal to the nearest tenth.

From 3.5

5. Explain how the graph of can be obtained from the graph of by means of translations, compressions, expansions, or reflections.

6. Given find the equations of any vertical, horizontal, or oblique asymptotes.

7.Given (from #6)

(a) Find the -intercept by evaluating .

(b) Find the -intercepts of .

(c) Will the graph cross its nonverticalasymptote?

(d) Use test points within the intervals formed by the verticalasymptotes-intercepts to determine the sign of in the interval.

(e) Graph .

From 3.6

8.For a body falling freely from rest (neglecting air resistance), the distance the body fallsvaries directly as the square of the time. If an object is dropped from a tower 400 ft high and hits the ground in 5 seconds, how far did it fall in the first 3 seconds?

9.The weight of an object varies inversely as the square of its distance from the center of the Earth. If an object at sea level (3978 mi from the center of the earth) weighs 220 lb, find its weight when it's 200 mi above the surface of the earth.

10. The volume of wood in a tree varies jointly as the height and the square of the girth . (girth is the distance around the tree.) If the volume of a redwood tree is when the height is 30 m and the girth is 1.5 m, what is the height of a tree whose volume is and girth is 2 m?