If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?
Practice Questions
1 question
Q1
If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?
f(x) = f(-x) for all x.
f(x) = -f(-x) for all x.
f(x) is always positive.
f(x) has a maximum value.
A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.
Questions & Step-by-step Solutions
1 item
Q
Q: If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?
Solution: A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.
Steps: 4
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, the output (y-value) for a positive input (x) must be the same as the output for the negative of that input (-x).
Step 3: Write down the property that describes this symmetry: f(x) = f(-x). This means that for every x, the function value at x is equal to the function value at -x.
Step 4: Conclude that if a function is symmetric about the y-axis, it must satisfy the property f(x) = f(-x) for all values of x.
