004- USMA(WP) entrance exam question independent variable

[karush]

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?

 

[Greg]

[8, 72]

 

[HallsofIvy]

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]

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]

Nothing is said, in this problem, about $$\theta$$ being the measure of an angle or any measurement at all. It's just a number.