Question

Use the key features of the polynomial f(x) = 5x2 − 2x − 3 to describe its end behavior.

a.The left side continues up, and the right side continues down.
b.The left side continues down, and the right side continues down.
c.The left side continues down, and the right side continues up.
d.The left side continues up, and the right side continues up.

Answer 1

D

Explanation:

The left side continues up, and the right side continues up.

Answer 2

d. The left side continues up, and the right side continues up.

Explanation:

We have been given a polynomial
`f(x)=5x^2-2x-3`. We are asked to describe the end behavior of our given polynomial.

We know that for a function of form
`f(x)=ax^n`, if n is even and
`a>0`, then

• The function approaches positive infinity (continues up) as x approaches negative infinity.

• The function approaches positive infinity (continues up) as x approaches positive infinity.

We know that for a function of form
`f(x)=ax^n`, if n is even and
`a<0`, then

• The function approaches negative infinity (continues down) as x approaches negative infinity.

• The function approaches negative infinity (continues down) as x approaches positive infinity.

We can see that for our given polynomial the value of 'n' is even and
`a=5`, which is greater than 0. So both sides of our given function continues up.

Therefore, option D is the correct choice.