# [SOLVED]004- USMA(WP) entrance exam question independent variable

#### karush

##### Well-known member
ok not sure what forum this was supposed to go in,,so...

If the independent variable of $W(\theta)=2\theta^2$ is restricted to values in the interval [2,6]
What is the interval of all possible values of the dependents variable?

Last edited:

Staff member
[8, 72]

#### HallsofIvy

##### Well-known member
MHB Math Helper
For positive values of $$\theta$$, $$\theta^2$$, and therefore $$2\theta^2$$, is an increasing function. Values of $$2\theta^2$$, for x between 2 and 6, lie between $$2(2^2)= 8$$ and $$2(6^2)= 72$$.

#### karush

##### Well-known member
For positive values of $$\theta$$, $$\theta^2$$, and therefore $$2\theta^2$$, is an increasing function. Values of $$2\theta^2$$, for x between 2 and 6, lie between $$2(2^2)= 8$$ and $$2(6^2)= 72$$.
Ok I think I got ???? Because $\theta$ ussually means radians or degrees!

#### HallsofIvy

##### Well-known member
MHB Math Helper
Nothing is said, in this problem, about $$\theta$$ being the measure of an angle or any measurement at all. It's just a number.