Question: If the graph of a function is symmetric about the y-axis, which of the following must be true?
Options:
The function is linear.
The function is even.
The function is odd.
The function has no intercepts.
Correct Answer: The function is even.
Solution:
A function is even if it is symmetric about the y-axis, meaning f(x) = f(-x) for all x.
If the graph of a function is symmetric about the y-axis, which of the following
Practice Questions
Q1
If the graph of a function is symmetric about the y-axis, which of the following must be true?
The function is linear.
The function is even.
The function is odd.
The function has no intercepts.
Questions & Step-by-Step Solutions
If the graph of a function is symmetric about the y-axis, which of the following must be true?
Step 1: Understand what symmetry about the y-axis means. This means that if you fold the graph along the y-axis, both sides will match perfectly.
Step 2: Recognize that for a function to be symmetric about the y-axis, it must satisfy a specific condition.
Step 3: The condition is that for every x value, the function's output at x must be the same as its output at -x. This can be written as f(x) = f(-x).
Step 4: Conclude that if a function is symmetric about the y-axis, it is classified as an 'even' function.
Even Functions – A function is classified as even if its graph is symmetric about the y-axis, which mathematically means that for every x in the domain, f(x) = f(-x).
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