The graph of $y = f(x)$ is shown below. For each point $(a, b)$ that is on the graph of $y = f(x),$ the point $\left( 3a - 1, \frac{b}{2} \right)$ is plotted, forming the graph of another function $y = g(x).$ As an example, the point $(0,2)$ lies on the graph of $y = f(x),$ so the point $(3 \cdot 0 - 1, 2/2) = (-1,1)$ lies on the graph of $y = g(x).$

(a) Plot the graph of $y = g(x).$ Include the diagram as part of your solution.

(b) Express $g(x)$ in terms of $f(x).$

(c) Describe the transformations that can be applied to the graph of $y = f(x)$ to obtain the graph of $y = g(x).$ For example, one transformation could be to stretch the graph vertically by a factor of $4.$

Order the numbers in each list from least to greatest. 0, |−14|, 13, −12, |−16|, 17

Aschool puts on a play. the play costs $1,200 in expenses. the students charge $4.00 for tickets. there will be one performance of the play in an auditorium that seats 500 people. what is the domain of the function that shows the profit as a function of the number of tickets sold?  

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?