Use the vertical line test to determine if the relation {(-6,-2), (-2,6), (0,3), (3,5)} is a function.
The graphs shows the number of handbags that Mandy makes in one day. What are the variables? Describe how the variables are related.
During a clothing store's Bargain Days, the regular price for T-Shirts is discounted to $8.25. You have an additional coupon $5.00 off, regardless how many shirts are purchased.
A. Write a rule for the function p(t) that expresses the final price of t T-Shirts with the discount applied.
B. How much would you pay during the Bargain Days for 11 shirts.
The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table linear?
Hours worked Amount Charged ($)
1 25
2 40
3 60
4 80
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To determine if the relation {(-6,-2), (-2,6), (0,3), (3,5)} is a function, we can use the vertical line test.
The vertical line test is a method used to determine if a graph represents a function. Imagine drawing a vertical line through the graph. If the vertical line intersects the graph at more than one point, then the relation is not a function. If the vertical line intersects the graph at only one point, then the relation is a function.
For the given relation {(-6,-2), (-2,6), (0,3), (3,5)}, we can plot these points on a graph and draw a vertical line. If the vertical line intersects the graph at more than one point, then the relation is not a function. If the vertical line intersects the graph at only one point, then the relation is a function.
Plotting the points on a graph, we get:
^
|
7 +
|
| o
6 + o
|
| o
5 + o
|
|
4 +
|
|
3 + o
|
|
2 +
|
+------+------+------+------+------+------+------+------+------+------+------->
-8 -6 -4 -2 0 2 4 6 8 10 12 14 16
As we can see from the graph, if we draw a vertical line, it intersects the graph at only one point for each x-value. Therefore, the relation {(-6,-2), (-2,6), (0,3), (3,5)} is a function.
Regarding the second question about the number of handbags that Mandy makes in one day, it seems there is no graph or specific relation given. If you provide more information or a specific question, I can attempt to assist you in understanding the variables and their relationship.
For the third question about the function p(t) that expresses the final price of t T-Shirts with the discount applied during Bargain Days:
A. The rule for the function p(t) can be expressed as:
p(t) = 8.25t - 5.00
Here, t represents the number of T-Shirts purchased, and p(t) represents the final price of t T-Shirts with the discount applied. The regular price of each T-Shirt is discounted to $8.25, and there is an additional coupon of $5.00 off.
B. To find out how much you would pay during Bargain Days for 11 shirts, substitute t = 11 into the function p(t):
p(11) = 8.25(11) - 5.00
= 90.75 - 5.00
= 85.75
Therefore, you would pay $85.75 during Bargain Days for 11 shirts.
Regarding the fourth question about the relationship shown by the data in the table for the carpenter's charging, we can examine whether the relationship is linear by analyzing the patterns in the data.
As the number of hours worked increases, we can observe that the amount charged also increases. The amount charged seems to increase by $15 for each additional hour worked. This constant increase indicates a linear relationship between the hours worked and the amount charged.
To further verify this, we can calculate the slope between the pairs of points using the formula:
slope = (change in y)/(change in x)
Calculating the slope between each pair of points:
Slope between (1, 25) and (2, 40):
slope = (40-25)/(2-1) = 15/1 = 15
Slope between (2, 40) and (3, 60):
slope = (60-40)/(3-2) = 20/1 = 20
Slope between (3, 60) and (4, 80):
slope = (80-60)/(4-3) = 20/1 = 20
As we can see, the slope is constant between each pair of points, indicating a fixed rate of increase. This confirms that the relationship shown by the data in the table is linear.