math

MATH 107 Quiz 3

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Each question is worth 5 points. Questions 1 – 5 are multiple choice; you do not need to show your work. Short answers for Questions 6 – 10; show your work to earn full credit – highlight answers in yellow or draw a box around the answer. You can insert additional lines if needed.

Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form and round decimals to hundredths. Write answers using positive exponents except when using scientific notation. Simplify all radicals and rationalize the denominators. Write complex numbers in the form a + bi. Applied problems must have the variables identified and an equation for full credit.

MULTIPLE CHOICE Check the box of the one alternative that best completes the statement or answers the question.

1.) Write equations of the horizontal and the vertical lines that pass through the point .

☐ horizontal: y = -8; vertical: x =

☐ horizontal: y = ; vertical: x = -8

☐ horizontal: y = x; vertical: x = -8y

☐ horizontal: y = - ; vertical: x = -8

☐ None of these

2.) Determine the intervals on which the function (to the left) is increasing, decreasing, and constant.

☐ Increasing on (-∞, 1); Decreasing on (1, ∞)

☐ Increasing on (1, ∞); Decreasing on (-∞, 1)

☐ Increasing on (-∞, -1); Decreasing on (-1, ∞)

☐ Increasing on (-1, ∞); Decreasing on (-∞, -1)

☐ None of these

3.) Given the function f, match the function g with a transformation of f.

f(x) = x2 – 3 and g(x) = x2 – 4

☐ f(x) + 1

☐ f(x – 1)

☐ f(x + 1)

☐ f(x) – 1

☐ None of these

4.) If an object is dropped off of a tower, the velocity, V, of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Express V as a linear function of t.

☐

☐ V(t) = 42t

☐ V(t) = 32(t + 10)

☐ V(t) = 32 + 10t

☐ None of these

5.) Fill in the blank:

Write an equation for a function that has a graph with the shape of y = x3 is shifted 3.2 units to the right and then vertically shrunk by a factor of 0.6.

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Short answers. You must show your work to earn full credit.

Highlight answers in yellow or draw a box around the answer.

6.) A deep sea diving bell is being lowered at a constant rate. After 10 minutes, the bell is at a depth of 300 feet. After 50 minutes the bell is at a depth of 1400 feet. What is the average rate of lowering per minute? Interpret the average rate of change of lowering per minute.

7.) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Use graphing calculator to determine the correlation coefficient? Does this indicate a good fit – why or why not? (Do not need to show work.)

8.) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Use a graphing calculator to model the data with a linear function that predicts the number of products sold as a function of the cost of advertising. Use the regression line to predict how many items would be sold if $7,000 is spent on advertising.

9.) Determine algebraically whether the function is even, odd, or neither even nor odd.

10.) Write a slope-intercept equation for a line that passes through (2, -7) and (6, -2).

In this Exercises find the cost and price-demand functions are given for different scenarios. For each scenario, Find the profit function P(x). Find the number of items which need to be sold in order to maximize profit. Find the maximum profit. Find the price to charge per item in order to maximize profit. Find and interpret break-even points.

11. The cost, in dollars, to produce x “I’d rather be a Sasquatch” T-Shirts is C(x) = 2x + 26, x ≥ 0 and the price-demand function, in dollars per shirt, is p(x) = 30 − 2x, 0 ≤ x ≤ 15.