What is the graph and what are the domain and range?

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 800 per day. The bus company charges $2.25 for a ride.They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.

What is the graph and what are the domain and range?
You have a point (2.25, 800) and a slope of 40/-0.25, or -160. The slope is a rate of change - if you lost 40 customers per $0.25, then your slope is 40/-0.25.





To find the equation of the line, use the point-slope formula:





y - y1 = m(x - x1)


y - 800 = -160(x - 2.25)


y - 800 = -160x + 360


y = -160x + 1160





The graph will be a line starting at (0, 1160) and going down with a slope of -160. The domain will start at 0 - since the x-axis represents money, you have to exclude negative numbers. To find the rightmost value for the domain, find the x-intercept:





0 = -160x + 1160


160x = 1160


x = 7.25





So your domain is [0, 7.25]. The range will be [0, 1160] - 0 for no customers, 1160 from the y-intercept.
Reply:Income is number of riders times the fare, I = RF. Let x be the number of $0.25 fare increases. Then I = (R-40x)(F+0.25x), and our intial values of R and F make our equation I = (800-40x)(2.25+0.25x). This is a parabola that opens downward, crossing the x-axis twice. The left x-intercept is the situation where the Income is 0 because the price has dropped to 0. The right x-intercept is the situation where the Income is 0 because the fare is so high there are no riders. What makes the problem an easy one, not needing calculus, is that the parabola is symmetric with respect to a vertical line through its vertex (max value), and that means the line of symmetry is exactly HALFWAY between those x-intercepts.





So, solving 800-40x = 0, the right intercept is x = 20. Solving 2.25 + .25x = 0, the left intercept is x = -9. Halfway between, x = 5.5. So the max income is 800(2.25 + 5.5(.25)) = 1800 + 1100 = 1900.





Since negative Income makes no sense, domain is -9 ≤ x ≤ 20 and range is 0 ≤ I ≤ 1900.
Reply:ok. so their income right now is 800 x 2.25, cuz 800 customers and 2.25 each. once they change it, say they increase it by 0.25, their customers would be (800-40) and their money per person would be (2.25+0.25). so then their income would be (800-40)(2.25+0.25). say they increase it again by 0.25 again. then their income would be


(800 - 40*2)(2.25 + 0.25*2). and if they increased it again, then income is (800 - 40*3)(2.25 + 0.25*3)





so if you made x=number of times they increase it, then their income would be given by


(800-40x)(2.25+0.25x)





now if you multiply that out using FOIL, you get


1800 + 200x - 90x - 10x^2.





so if you wanted to find the graph of this, you have to complete the square.


-10x^2 + 110x + 1800


= -10 (x^2 - 11x -180)


= -10 (x^2 - 11x + 30.25 - 30.25 - 180)


(30.25 is half of 11 squared)





= -10 (x-5.5)^2 - 2102.5





so the maximum would be when x=5.5, so the increase would be 5.5 * 0.25 which is 1.375 or $1.38.





the domain would be all x, since x can be anything.


the range would be y%26lt;5.5, since the maximum is when x=5.5 so all other values have to be less than that.








another way to graph it is to find the x intercepts, which are the roots of (800-40x)(2.25+0.25x) which means x = 800/40 = 20 and x = -2.25/0.25 = -9. and then find the y intercept, which is when x=0, so its 1800. and then differentiate the function (take the derivative)


-10x^2 + 110x + 1800 to get


-20x + 110 and set that to 0 to find where the function has a maximum (youll get x=5.5 again). and ya.





anywayz, hope that helps. laterz
Reply:The range is the what ever goes on the y-axis for example if in a graph you are going by 10 the range will be 10 20... and domain is the x-axis.
Reply:i'm not sure about the domain and range, but the graph is, in slope-intercept form, y = -.25x + 1160, i think.
Reply:The Domain is the number on the graph that is the x-variable, and the range is a y-variable. Like when you have an ordered pair (3,-2) then the three is the domain and the (-2) is the range.