Question
If you were ONLY given the graph of the function, how could you determine if the function was even, odd, or neither? Use at least two sentences to support your answer.
Ask by Chavez Bowman. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To determine if a function is even, check for symmetry about the y-axis. For an odd function, look for symmetry about the origin. If neither symmetry is present, the function is neither even nor odd.
Solution
To determine if a function is even, observe whether its graph is symmetric about the y-axis; this means that every point (x, y) on the graph has a corresponding point (-x, y). For an odd function, check if the graph is symmetric about the origin, meaning every point (x, y) has a corresponding point (-x, -y). If the graph does not clearly show either of these types of symmetry, the function is likely neither even nor odd.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To determine if a function is even, odd, or neither using only its graph, you can visually assess its symmetry. A function is even if it is symmetric about the y-axis, meaning that for every point (x, y), there is also a corresponding point (-x, y). Conversely, a function is odd if it exhibits rotational symmetry around the origin, so that for every point (x, y), there exists a point (-x, -y). If the graph does not conform to either of these symmetry properties, the function can be classified as neither even nor odd.
