a) You can graph the function by identifying some key points of the function and making a table for points. You can calculate the y-intercept by substituting x with 0, which would be 7/11. For the rest of the points, simply make a table like this:
Afterwards, you would plot these points and connect them with a smooth line, which would look like this: (make sure to scale your graph axis correctly)
b) In the context of this problem, only the first quadrant of the graph would be meaningful. As a kicker can't make negative numbers of consecutive field goals and there can't be a negative field goal percentage, both of the x and f(x) values should be positive. In the first quadrant, both x and f(x) values are positive.
c) For this question, you need to realise what y-intercept represents. Graphically, it is where it crosses the vertical axis, but it also represents a y-value when x=0. In terms of this question, x=0 means that no more extra consecutive field goals were scored. This means that the y-intercept represents the kicker's original field goal percentage (7/11).
d) Remember, when the leading power of the numerator and the denominator are equal, the horizontal asymptote is the ratio between the numerator and the denominator's leading coefficient. In this question, it would be 1/1 = 1, which would be y=1. As the graph never actually touches the asymptote, this represents that Eduardo would never have a field goal percentage of 1 (which is 100%).
Question 2.
a) You need to really understand what average means in this question. In this case, average cost would be (total cost) / (total number of people who are actually paying). Total cost would equal to fixed cost plus variable cost. Fixed cost is like a set-up fee and variable cost is a type of cost that depends on the amount of production (ex: per person). So, for this question, total cost would be 75+9.50x. For the total number of people, you have to make sure that each of the 15 council members would get one for free. So, it would be x-15. Hence, the function would be f(x) = (75+9.50x)/(x-15).
You can graph the function like how said earlier, and you would get a graph like this:
b) You can find the average cost by substituting values into the equation or through the graph. I'll do it through the equation. For 200 shirts, it would be (75+9.5*200)/(200-15) = $10.68. For 500 shirts, it would be (75+9.5*500)/(500-15) = $9.95.
c) Now, you can substitute 9.75 into the y value to calculate for x (number of orders).
9.75 = (75+9.50x)/(x-15)
(75+9.50x) = 9.75(x-15)
(75+9.50x) = 9.75x-146.25
0.25x = 221.25
x = 885.
So at least 885 shirts must be ordered to bring the average cost under $9.75.
Sorry for such a lengthy response. Does this answer your question?
Hi, thank you for your question.
Question 1.
a) You can graph the function by identifying some key points of the function and making a table for points. You can calculate the y-intercept by substituting x with 0, which would be 7/11. For the rest of the points, simply make a table like this:
Afterwards, you would plot these points and connect them with a smooth line, which would look like this: (make sure to scale your graph axis correctly)
b) In the context of this problem, only the first quadrant of the graph would be meaningful. As a kicker can't make negative numbers of consecutive field goals and there can't be a negative field goal percentage, both of the x and f(x) values should be positive. In the first quadrant, both x and f(x) values are positive.
c) For this question, you need to realise what y-intercept represents. Graphically, it is where it crosses the vertical axis, but it also represents a y-value when x=0. In terms of this question, x=0 means that no more extra consecutive field goals were scored. This means that the y-intercept represents the kicker's original field goal percentage (7/11).
d) Remember, when the leading power of the numerator and the denominator are equal, the horizontal asymptote is the ratio between the numerator and the denominator's leading coefficient. In this question, it would be 1/1 = 1, which would be y=1. As the graph never actually touches the asymptote, this represents that Eduardo would never have a field goal percentage of 1 (which is 100%).
Question 2.
a) You need to really understand what average means in this question. In this case, average cost would be (total cost) / (total number of people who are actually paying). Total cost would equal to fixed cost plus variable cost. Fixed cost is like a set-up fee and variable cost is a type of cost that depends on the amount of production (ex: per person). So, for this question, total cost would be 75+9.50x. For the total number of people, you have to make sure that each of the 15 council members would get one for free. So, it would be x-15. Hence, the function would be f(x) = (75+9.50x)/(x-15).
You can graph the function like how said earlier, and you would get a graph like this:
b) You can find the average cost by substituting values into the equation or through the graph. I'll do it through the equation. For 200 shirts, it would be (75+9.5*200)/(200-15) = $10.68. For 500 shirts, it would be (75+9.5*500)/(500-15) = $9.95.
c) Now, you can substitute 9.75 into the y value to calculate for x (number of orders).
9.75 = (75+9.50x)/(x-15)
(75+9.50x) = 9.75(x-15)
(75+9.50x) = 9.75x-146.25
0.25x = 221.25
x = 885.
So at least 885 shirts must be ordered to bring the average cost under $9.75.
Sorry for such a lengthy response. Does this answer your question?