Question

What is the end behavior of the graph of f(x) = – 0.5x^2 – 3x – 4?

Answer 1

We will see that as x tends to ± ∞, the function tends to -∞.

• for  x ⇒ ∞, f(x)  ⇒ -∞
• for  x ⇒ -∞, f(x)  ⇒ -∞.

What is the end behavior?

We define the end behavior as how the function behaves as x tends to very large, in absolute value, values.

In this case we have a quadratic equation:

f(x) = -0.5*x^2 - 3*x - 4

Here you can see that the leading coefficient is negative, thus, the arms of the graph will go downwards.

This means that in the limits of x ⇒ ∞ and x ⇒ -∞, the function will tend to negative infinity.

Then the end behavior can be written as:

• for  x ⇒ ∞, f(x)  ⇒ -∞
• for  x ⇒ -∞, f(x)  ⇒ -∞.

If you want to learn more about end behavior, you can read:

brainly.com/question/11275875