On the set of axes below, graph the function represented by y=cubed root of x-2 for the domain -6< or equal to x< or equal to 10.
x column I did -6, 1, 2 , 3 ,10
y column I did -2, -1, 0, 1, 2
Then I plotted these points.
Is this correct?
Thanks for checking over my work.
no way for me to see. However, check your graph against this one:
http://www.wolframalpha.com/input/?i=y%5E3+%3D+x-2
To graph the function y = cubed root of x - 2 for the given domain -6 ≤ x ≤ 10, you need to calculate the corresponding values of y for each x-value in the domain.
Using the x-values you provided: -6, 1, 2, 3, 10
Substituting these x-values into the function:
When x = -6, y = cubed root of (-6) - 2 = -2 - 2 = -4
When x = 1, y = cubed root of (1) - 2 = 1 - 2 = -1
When x = 2, y = cubed root of (2) - 2 = 1 - 2 = -1
When x = 3, y = cubed root of (3) - 2 = 1 - 2 = -1
When x = 10, y = cubed root of (10) - 2 = 2 - 2 = 0
Based on these calculations, the corresponding y-values are -4, -1, -1, -1, and 0, respectively.
So, the points you have plotted for the x and y values (-6, -2), (1, -1), (2, -1), (3, -1), and (10, 0) are correct.
To complete the graph, plot these points on the set of axes and connect them with a smooth curve. Make sure to also include the points at the boundaries of the domain, which are (-6, -2) and (10, 0).
Overall, your work seems correct based on the given information.
Based on the information you provided, it seems like you have correctly plotted the points on the graph. However, before confirming that it is correct, let's go through the process of graphing the function step by step to make sure.
First, let's find the y-values for the given x-values using the function y = ∛(x - 2). I'll use the same x-values you provided:
For x = -6: y = ∛(-6 - 2) = ∛(-8) = -2
For x = 1: y = ∛(1 - 2) = ∛(-1) ≈ -1
For x = 2: y = ∛(2 - 2) = ∛(0) = 0
For x = 3: y = ∛(3 - 2) = ∛(1) = 1
For x = 10: y = ∛(10 - 2) = ∛(8) ≈ 2
Now, let's plot these points on the graph:
Point A: (-6, -2)
Point B: (1, -1)
Point C: (2, 0)
Point D: (3, 1)
Point E: (10, 2)
After plotting these points, connect them in a smooth curve. Make sure to label the axes and any important points.
Now, if your plotted points and the graph match the points we found earlier, then your work is correct. Double-check the accuracy of your plotting and the scale of your graph. If everything matches up, you have successfully graphed the function!
I hope this explanation helps you understand the process of graphing the function y = ∛(x - 2) for the given domain. If you have any more questions, feel free to ask!