Q: A monthly tablet plan costs $$34.99 for up to 3 GB of data, and 15$ per additional GB. Which function correctly models the monthly cost C(x$$)$$ for x$ GB of data?

$$C(x) = \begin{cases} 34.99 & 0 \leq x \leq 3 \\ 15x - 10.01 & x \u003e 3 \end{cases}$$

Question 1

A rock is dropped from a height of 20 meters. Its height after $$x$$ seconds is given by $$H(x) = 20 - 4.9x^2$. After how many seconds does the rock hit the ground?

Accepted Answer

$$x = 2.02$$ seconds

Question 2

Given the function $$H(x) = 20 - 4.9x^2$, what is the height of the rock at x = 1.2$ seconds?

Accepted Answer

$$H(1.2) = 12.94$$ meters

Question 3

A monthly tablet plan costs $$34.99 for up to 3 GB of data, and 15$ per additional GB. Which function correctly models the monthly cost C(x$$)$$ for x$ GB of data?

Accepted Answer

$$C(x) = \begin{cases} 34.99 & 0 \leq x \leq 3 \ 15x - 10.01 & x \u003e 3 \end{cases}$$

Question 4

Using the tablet plan cost function $$C(x)$$, what is the monthly cost for using 5 GB of data?

Accepted Answer

$$C(5) = 64.99$$

Question 5

The demand $$D$$ for candy at a movie theater is inversely related to the price $$p. If$$ $$D = 156$$ when $$p = 2.75$$, what is the demand function?

Accepted Answer

$$D = \frac{429}{p}$$

Question 6

If the price of candy is raised to $$3$$ per bag, how many bags will be sold according to the demand function $$D = \frac{429}{p}$$?

Accepted Answer

$$143$$ bags

Question 7

Given the graph of $$f$$ with points $$(-6, -3)$$, $$(0, 3)$$, $$(2, 4)$$, $$(4, 3)$$, $$(6, 0)$$, $$(8, -2)$$, $$(10, 0)$$, and $$(11, 1)$$, what is the domain of $$f$$?

Accepted Answer

$$[-6, 11]$$

Question 8

For the function $$f in $$the graph, for what values of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$x = 0, 6, 10$$

Question 9

Given the function $$f$$ graphed with $$f(0) = 3$$ and $$f(2) = 4$$, what is the $$y-$$intercept of $$f$$?

Accepted Answer

$$3$$

Question 10

For the function graphed in problem 25, what is the range of $$f$$?

Accepted Answer

$$[0, 3] \cup \{2\}$$

Question 11

For the function in problem 25, is the function even, odd, or neither?

Accepted Answer

Even

Question 12

The distance $$s$$ that an object falls is directly proportional to the square of the time $$t. If$$ $$s = 16$$ when $$t = 1$$, how far will it fall in $$3$$ seconds?

Accepted Answer

$$s = 144$$ feet

Question 13

For the function $$H(x) = 20 - 4.9x^2$, at what time is the height of the rock 10$ meters?

Accepted Answer

$$x = 1.43$$ seconds

Question 14

Given the piecewise function $$C(x)$$ for the tablet plan, what is the cost for $$13 GB of $$data?

Accepted Answer

$$C(13) = 184.99$$

Question 15

For the function $$f$$ graphed in problem 11, for what values of $$x$$ does $$f(x) = -2$$?

Accepted Answer

$$x = -5, 8$$

Question 16

For the function $$f$$ graphed in problem 11, what is the maximum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Maximum value is $$4 at$$ $$x = 2$$

College Algebra Study Guide: Functions, Graphs, and Applications

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