# Thread: FUNCTIONS??? No clue how to do these.

1. ## FUNCTIONS??? No clue how to do these.

ok, one of the "easier" ones...

what is the range of the function, f(x )= 2x² - 7x + 1 , -2 ≤ x ≤ 3

thanks in advance to anyone who can help

2. Originally Posted by juliak
ok, one of the "easier" ones...

what is the range of the function, f(x )= 2x² - 7x + 1 , -2 ≤ x ≤ 3

thanks in advance to anyone who can help
remember, the range is the set of y-values for which your function is defined, given some domain. on an unrestricted domain, a parabola where the coefficient is positive has range $[ \text{vertex}, \infty)$. so start there, but note that you can't go all the way up to $\infty$ here, since your domain is restricted

3. ok yeah i see that, but where do i start to figure it out?
i get that the second part restricts it, but where do i go from there?

4. You want the maxima and minima of the function.
Find the local extrema and see if it is between -2 and 3 and evaluate f(-2) and f(3). The minimal value is your minima, same for maxima and these are the boundaries of the range.

5. Originally Posted by vincisonfire
You want the maxima and minima of the function.
Find the local extrema and see if it is between -2 and 3 and evaluate f(-2) and f(3). The minimal value is your minima, same for maxima and these are the boundaries of the range.
As Jhevon pointed out, the minimum value (y-coordinate of vertex) is the lower boundary of the range. The upper boundary will be f(-2) or f(3), whichever yields the largest value for y.