Question

ap pre - calculus and uad polynomials

1. state whether the following graphs represent functions that are even, odd, or neither.

2.
3.
ca #1

Explanation:

Step1: Recall function - symmetry rules

A function \(y = f(x)\) is even if \(f(-x)=f(x)\) (symmetric about the y - axis) and odd if \(f(-x)=-f(x)\) (symmetric about the origin).

Step2: Analyze the first graph

For the first graph, if we reflect the graph about the origin, it coincides with itself. Let \(y = f(x)\). For every point \((x,y)\) on the graph, the point \((-x, - y)\) is also on the graph. So \(f(-x)=-f(x)\), and it is an odd function.

Step3: Analyze the second graph

For the second graph, if we reflect it about the y - axis, it does not coincide with itself. Also, if we reflect it about the origin, it does not coincide with itself. So it is neither even nor odd.

Step4: Analyze the third graph

For the third graph, if we reflect the graph about the y - axis, it coincides with itself. Let \(y = f(x)\). For every point \((x,y)\) on the graph, the point \((-x,y)\) is also on the graph. So \(f(-x)=f(x)\), and it is an even function.

Answer:

1. Odd
2. Neither
3. Even