what is the range of 2x^2-4x-7

Question

the whole question asks: State the domain and range of the function. (Enter your answers using interval notation.)
f(x) = 2x^2 − 4x − 7. the domain is all real numbers, but i don't know what the range would be

Answer 1

Cassandra,

 

You can look at the function piecemeal

f(x) = (2x2) + (-4x -7)  so you have a quadratic added to a straight line in the form y = mx + b = -4x -7.

Now we know that the range of a straight line is all the positive and negative real numbers and zero (i.e, all reals).  So whatever range is added by the second function (y>=0) doesn't change the contribution from the line, just emphasizes a part of it. Thus,

 

Range of f(x) = Range of (2x2)  +  Range of (-4 - 7)

                    = y>=0               +   all y reals

                    = all y reals  =  y < 0 and y >= 0

Answer 2

All real numbers too

 

Answer 3

Hi Cassandra, here is the most simple way to understand it:

 

domain = x-values

range   =  y-values or f(x) in this case.

 

As you can see the equation (function), it is indefinite.

Whatever you put for x, you will get the y f(x).

 

both are all real numbers.

 

-∞ < y < ∞

 

Good luck.

Answer 4

I suggest graphing a few points to see what this looks like.  That gives you the answer. The below might help you see the answer.

 

For x =0, fx = -7

 

For x = 1, fx = -9

For x = -1, fx =-1

 

for  x = 2, fx = -7

for x = -2, fx = 9

 

for x = 3, fx = -1

for x = -3,fx = 23

 

for x = 10, fx = 153

for x=-10, fx = 233