Hello!
We are going to determine the degree and end behavior of the function given.
The function that was given was:
f(x) = 8x^3 + 2x^4 - 5x^2 + 9
Solve:
To determine the degree of the function, it will be the highest degree of the function, or in other words, the highest exponent.
In this case, the highest exponent in our function is "4", therefore it makes this a 4th-degree polynomial.
To determine the end behavior of the function, we can analyze its graph and determine the direction of the function. We will evaluate the function when x approaches -∞ and +∞.
When looking at the graph, as x → +∞ (meaning as x approaches positive infinity), the graph goes in the positive direction (up), and since it goes on forever, it goes in the positive direction infinitely. Therefore, we can write this as: as x → +∞, f(x) → +∞
When looking at the graph, as x → -∞ (meaning as x approaches negative infinity), the graph goes in the positive direction (up), and since it goes on forever, it goes in the positive direction infinitely. Therefore, we can write this as: as x → -∞, f(x) → +∞
Answer:
Degree of the function: 4th degree (4).
End behaviors:
- as x → +∞, f(x) → +∞
- as x → -∞, f(x) → +∞
You can also write the end behaviors as:
- as x → ∞, f(x) → ∞
- as x → -∞, f(x) → ∞