(All Steps) a) Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the

Question: a)

Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.

Graph Type Parabola

Explanation The graph corresponds to a parabola, because it has the structure of a traditional parabola (one vertex, without any concavity change)

Domain The domain is all the real numbers $\mathbb{R}$

Range The range is $[2,\infty )$

x	-2	-1	0	1	2
y	.25	.5	1	2	4

Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.

Graph

Graph Type            Exponential

Explanation The graph corresponds to an exponential because it’s always increasing, with no concavity changes, and it crosses the y axis at $y=1$.

Domain      All real numbers $\mathbb{R}$.

Range         $(0,\infty )$

Given the graph above, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.

Graph Type      Hyperbola

Explanation       The graph corresponds to a hyperbola because it has the corresponding asymptote lines and symmetry with respect to those lines.

Domain            The domain is all the real numbers except for 0: $\mathbb{R}\backslash \{0\}$

Range               The range is all the real numbers except for 0: $\mathbb{R}\backslash \{0\}$

d) In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.

Given the description above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph you have drawn, and also the domain and range of the entire function excluding unrealistic values. The vertical axis is the number of riders per day, and the horizontal axis is the fare.

Graph

Graph Type Linear

Explanation The function is a linear function, with slope equal to

\[m=\frac{-50}{0.25}=-200\]

The equation is therefore:

\[y-2000=-200(x-2)\Leftrightarrow y-2000=-200x+400\] \[\Leftrightarrow y=-200x+2400\]

Domain $[0,12]$ (The function is well define for all real numbers, but the number of people would be negative if the price is greater than $12, which doesn’t make sense)

Range [0,2400] (This is considering that the domain is [0,12])

2) For the function,

\[y=\frac{1}{x-1}\]