A few inequality questions: find domain, range of fcns

[fred2028]

I'm stuck on this one.
9) Find the [...] range of f if -2 < x < 3 and f(x) = x^2 - 2x.

This is what I've tried:

-2 < x < 3
-2x < x^2 < 3x
-2x - 2x < x^2 - 2x < 3x - 2x
0 < x^2 - 2x < x

I don't know how to continue. Also, number 10 stumped me too.

10) The function h(t) = -4.9t^2 - 24.5t models the height, h, of a golf ball above the ground in meters, t seconds after the ball is hit. Find the domain of this function.

I'm sorry, but I don't know how to go about this at all, so I have no work to show for number 10

 

[stapel]

9) Since x might be negative, there is no way to "multiply through" by x on the inequality.

Instead, draw the graph of f(x), and look at the y-values that are covered by f over the x-inverval (-2, 3). Finding the vertex and the values of f(-2) and f(3) will probably be useful.

10) The "domain" is all allowable x-values. What x-values make sense for this function, in light of the meaning of t and h?

Again, looking at the graph would probably be useful.

Eliz.

 

[fred2028]

OK thanks guys, problem solved