Determine whether the function is even, odd, or neither. Then determine whether the function’s 9

Determine whether the function is even, odd, or neither. Choose the correct answer below.
odd
neither
even
Determine whether the graph of the function is symmetric with respect to the -axis, the origin, or t
neither
y-axis

Question

Determine whether the function is even, odd, or neither. Then determine whether the function’s 9

Determine whether the function is even, odd, or neither. Choose the correct answer below.
odd
neither
even
Determine whether the graph of the function is symmetric with respect to the

-axis, the origin, or t
neither
y-axis

UpStudy AI · Accepted Answer

**Step 1. Check for evenness or oddness**

We have $$ h(x) = x^6 - x^8 $$.

- For an even function, we need $$ h(-x) = h(x) $$.
- For an odd function, we need $$ h(-x) = -h(x) $$.

Compute $$ h(-x) $$:
$$
h(-x) = (-x)^6 - (-x)^8
$$
Since $$ (-x)^6 = x^6 $$ (because 6 is even) and $$ (-x)^8 = x^8 $$ (because 8 is even), we have:
$$
h(-x) = x^6 - x^8 = h(x)
$$

Since $$ h(-x) = h(x) $$, the function is even.

**Step 2. Determine the symmetry of the graph**

Even functions are symmetric with respect to the $$ y $$-axis.

**Final Answers:**

- The function is **even**.
- Its graph is symmetric with respect to the **$$ y $$-axis**.
The function $$ h(x) = x^6 - x^8 $$ is **even** and its graph is symmetric with respect to the **$$ y $$-axis**.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions