Choose the correct answer below.

Question

Determine whether each statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement. No quadratic functions have a range of ​(−∞​, ∞​).

A.

The statement is true.

B.

The statement is false. A true statement is​ "All quadratic functions have a range of (−∞​,∞​)."

C.

The statement is false. A true statement is​ "The quadratic functions for which a>​0, have a range of (−∞​,∞​)."

D.

The statement is false. A true statement is​ "The quadratic functions for which a<​0, have a range of ​(−∞​,∞​)."

Answer 1

TL; DR The answer is A.

Quadratic functions have a degree of two.

This means the range will always either tend towards - ∞ or + ∞, but not both.

Think about some cases:

a>0

2x²+x+1. at extreme positive or negative values (x=10000000/-1000000000) this function tends towards +∞ and not to -∞

a<0

-2x²-x+1. at extreme positive or negative values (x=1000000/-10000000) this function tends towards -∞ and not to +∞.

Hope this helps, let me know if you have further questions.