How am I supposed to graph the following functions?
1. A wholesaler is buying auto parts. He has $200 to spend. He receives 5 parts free with the order. The number of parts y he can buy, if the average price of the parts is x dollars, is y = 200/x + 5.
a. Graph the function.
A: ?
2. A caterer has $100 in her budget for fruit. Slicing and delivery of each y = 100/x + 5 represents the number of pounds y she can buy.
a. Graph the function.
A: ?
well, shoot. How do you graph any function? You pick some values for x, compute the value for y, and plot some points. Then draw a curve through the points.
For y = 200/x + 5, start with x=1 and figure a few points.
x y
1 205
2 105
3 71.7
4 55
and so on.
To graph the given functions, we can follow these steps:
1. Understand the function:
- In both cases, we have a formula to determine the number of parts/fruit the buyer can afford based on the average price per unit.
- Both functions have the form y = 200/x + 5 (where 200 is the budget amount and 5 represents the free items/added cost).
2. Choose suitable values for x:
- We need to select several suitable values for x (average price) to plot the points on the graph.
- Take care to ensure the values cover a reasonable range that reflects the problem at hand.
3. Calculate corresponding values for y:
- Plug each chosen x value into the function and calculate the respective y value.
- For example, if x = 10, substitute it into the function: y = 200/10 + 5 = 25 + 5 = 30.
- Calculate the corresponding y values for each chosen x.
4. Plot the points:
- Using the selected values for x and their corresponding y values, plot the points on a graph.
- The horizontal axis represents the average price (x) and the vertical axis represents the number of items (y).
- Make sure to label the axes appropriately.
5. Connect the points:
- After plotting all the points, connect them using a smooth curve.
- A curve makes sense in this context because the function is continuous.
Now let's apply these steps to each given function:
1. The function for the number of parts is y = 200/x + 5.
- Choose values for x: Let's select the range as x = 10, 20, 30, 40, 50, 60.
- Calculate corresponding y values:
- For x = 10, y = 200/10 + 5 = 20 + 5 = 25.
- For x = 20, y = 200/20 + 5 = 10 + 5 = 15.
- For x = 30, y = 200/30 + 5 = 6.67 + 5 = 11.67 (approximated).
- For x = 40, y = 200/40 + 5 = 5 + 5 = 10.
- For x = 50, y = 200/50 + 5 = 4 + 5 = 9.
- For x = 60, y = 200/60 + 5 = 3.33 + 5 = 8.33 (approximated).
- Plot the points (x,y): (10, 25), (20, 15), (30, 11.67), (40, 10), (50, 9), (60, 8.33).
- Connect the points with a smooth curve.
- Label the axes as "Average Price ($)" for x and "Number of Parts" for y.
2. The function for the number of pounds is y = 100/x + 5.
- Choose values for x: Let's select the range as x = 10, 20, 30, 40, 50, 60.
- Calculate corresponding y values:
- For x = 10, y = 100/10 + 5 = 10 + 5 = 15.
- For x = 20, y = 100/20 + 5 = 5 + 5 = 10.
- For x = 30, y = 100/30 + 5 = 3.33 + 5 = 8.33 (approximated).
- For x = 40, y = 100/40 + 5 = 2.5 + 5 = 7.5.
- For x = 50, y = 100/50 + 5 = 2 + 5 = 7.
- For x = 60, y = 100/60 + 5 = 1.67 + 5 = 6.67 (approximated).
- Plot the points (x,y): (10, 15), (20, 10), (30, 8.33), (40, 7.5), (50, 7), (60, 6.67).
- Connect the points with a smooth curve.
- Label the axes as "Average Price ($)" for x and "Number of Pounds" for y.
Remember, the resulting graphs will provide a visual representation of the relationship between average price and the number of parts/fruits the buyers can afford within the given budget.