QuestionGraphically analyze if the function is even, odd, or neither.
Studdy Solution
STEP 1
Assumptions1. The function given is .
. We are to determine graphically if the function is even, odd, or neither.
3. An even function is symmetric about the y-axis, meaning for all x in the domain of f.
4. An odd function is symmetric about the origin, meaning for all x in the domain of f.
STEP 2
First, let's plot the function to visually inspect its symmetry.
Unfortunately, as an AI, I can't physically plot a graph. However, I can explain how to do it.1. Choose a range of x-values, both positive and negative. For example, you might choose -, -2, -1,0,1,2,.
2. For each x-value, calculate the corresponding y-value using the function .
. Plot these points on a graph and draw a smooth curve through them.
STEP 3
Once you have the graph, check for symmetry.
1. If the graph is symmetric about the y-axis (meaning the left and right halves of the graph are mirror images of each other), then the function is even.
2. If the graph is symmetric about the origin (meaning the graph in the second quadrant is a mirror image of the graph in the fourth quadrant, and the graph in the first quadrant is a mirror image of the graph in the third quadrant), then the function is odd.
3. If the graph is not symmetric about either the y-axis or the origin, then the function is neither even nor odd.
STEP 4
By plotting the function , you will find that the graph is symmetric about the origin. Therefore, the function is odd.
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