# Thread: Range of a Function with a Prescribed Domain

1. ## Range of a Function with a Prescribed Domain

Can someone explain how I can find the range of a function with a prescribed domain.

E.X
f(x) = 2x^2 + 4 for –3 < x < 5. What is the range of f?
f(x) = 1/x for -2 < x < 3 What is the range of f?

3. Originally Posted by ferken
Can someone explain how I can find the range of a function with a prescribed domain.

E.X
f(x) = 2x^2 + 4 for –3 < x < 5. What is the range of f?
f(x) = 1/x for -2 < x < 3 What is the range of f?

Use the minimum and maximum values of your domain and apply them to f(x) to obtain min and max values for your range.

$\displaystyle f(-3)=2(-3)^2+4=22$

$\displaystyle f(5)=2(5)^2+4=54$

The vertex of the parabola is the minimum point of y=4

$\displaystyle y=2x^2+4$

$\displaystyle y=2(x-0)^2+4$

Vertex is at (0, 4)

The range of your first example: $\displaystyle \{y|4<y<54\}$

4. Originally Posted by masters
Use the minimum and maximum values of your domain and apply them to f(x) to obtain min and max values for your range.

$\displaystyle f(-3)=2(-3)^2+4=22$

$\displaystyle f(5)=2(5)^2+4=54$

The range of your first example: $\displaystyle \{y|22<y<54\}$
Thankyou for the help, however the answer for example 1 is
f(x) is {4 < f(x) < 54}.

So now im even more confused!

Hello Ferken,

The function, $\displaystyle f(x) = 2x^2+4$ is an upward parabola whose minimum value is 4 when x = 0.

Here, f(0) = 4

f(-3) = 22

and f(5) = 54

so, Range $\displaystyle = \{f(x)|4<f(x)<54\}$

Please see the attached graph for more clarification.

Now, do the second question in the same way.

Did you get it now ???

6. Originally Posted by ferken
Thankyou for the help, however the answer for example 1 is
f(x) is {4 < f(x) < 54}.

So now im even more confused!
You are absolutely right, ferken. I forgot about the minimum point at the vertex. Thanks for pointing that out. It's been a long day. I edited my post to reflect the correct range.

7. Thankyou for helping me.
I now understand how to do the questions, and yes i can do question 2 in my example now.

Thanks for all the help !