# Thread: finding range of function

1. ## finding range of function

The function g is defined by $g(x) = x^{2} -8x +17$,

$0\leq x$

Find the range of g.

How do I find this? Is there a particular 'technique'?

Thanks,

2. Originally Posted by Tweety
The function g is defined by $g(x) = x^{2} -8x +17$,

$0\leq x$

Find the range of g.

How do I find this? Is there a particular 'technique'?

Thanks,
hi
since your function has no real roots,the parabola is strictly above the X-axis.

3. Originally Posted by Raoh
hi
since your function has no real roots,the parabola is strictly above the X-axis.
Thanks,

So the range is all the values greater than or equal to zero?

4. if you're able to find a global minimum for your function then i think you can find the range.

5. Originally Posted by Tweety
Thanks,

So the range is all the values greater than or equal to zero?
i think Strictly greater than zero.
if we solve f'(x)=0.we'll find x=4 as a solution and at this point there is a global minimum.
f(4)=1.
therefore,the range is, $[1,\infty )$
i might be wrong though...

6. Originally Posted by Tweety
The function g is defined by $g(x) = x^{2} -8x +17$,

$0\leq x$

Find the range of g.

How do I find this? Is there a particular 'technique'?

Thanks,
Draw the graph. Hint: Complete the square first.