Compare the functions
y = x^2 and y= |x |
Provide a table of vaules for both functions and graph
To compare the functions y = x^2 and y = |x|, we can create a table of values and graph them.
Table of Values:
For y = x^2:
x | y
-3 | 9
-2 | 4
-1 | 1
0 | 0
1 | 1
2 | 4
3 | 9
For y = |x|:
x | y
-3 | 3
-2 | 2
-1 | 1
0 | 0
1 | 1
2 | 2
3 | 3
Graph:
The graph of y = x^2 will be a parabola with the vertex at (0, 0) and opening upwards.
The graph of y = |x| will be a V-shape, with the vertex at (0, 0), and the arms pointing upwards.
Below is a graph comparing both functions. The blue line represents y = x^2, and the orange line represents y = |x|.
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-3-2-10123
From the graph and the table of values, we can see that for positive values of x, the values of y for both functions are the same since the absolute value of a positive number is the number itself. However, for negative values of x, the values of y for y = |x| are positive, whereas the values of y for y = x^2 are negative since squaring any negative number results in a positive number.
Therefore, the main difference between the two functions is that y = x^2 will always give positive values or zero, while y = |x| can give both positive and negative values.