 determine  whether each  function  is  even, odd, or neither for f(x)=x squared-1 

To determine whether a function is **even**, **odd**, or **neither**, we can apply the following tests:

1. **Even function:** A function \( f(x) \) is even if \( f(-x) = f(x) \) for all \( x \).
2. **Odd function:** A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \).

Given the function:
\[
f(x) = x^2 - 1
\]

### Step 1: Test for Even Function
Substitute \( -x \) into the function:
\[
f(-x) = (-x)^2 - 1 = x^2 - 1
\]

Since \( f(-x) = f(x) \), the function satisfies the condition for being **even**.

### Step 2: Test for Odd Function
Now, check if the function is odd by seeing if \( f(-x) = -f(x) \):
\[
f(-x) = x^2 - 1
\]
\[
-f(x) = -(x^2 - 1) = -x^2 + 1
\]

Since \( f(-x) \neq -f(x) \), the function is **not odd**.

### Conclusion:
The function \( f(x) = x^2 - 1 \) is **even**.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore:

1. How do we test for odd and even functions with more complex expressions?
2. What types of graphs do even and odd functions typically have?
3. Can a function be both even and odd?
4. How would transformations (like shifting the graph) affect whether a function is even or odd?
5. What is the significance of even and odd functions in calculus?

**Tip:** Even functions are symmetric with respect to the y-axis, while odd functions are symmetric around the origin.

determine whether each function is even, odd, or neither for f(x)=x squared - 1

Explore how to determine if the function f(x) = x^2 - 1 is even, odd, or neither. This step-by-step solution walks through algebraic tests for symmetry, covering even and odd functions. Ideal for students in Grades 9-12 studying algebraic functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation