# Math Insight

### Functions and inequalities worksheet

#### Functions

Let $f(x) = 3x^2$. What is $f(2)$?

Let $g(\bigstar) = 3\bigstar^2$. What is $g(2)$?

Let $h(\pitchfork) = \bowtie \pitchfork^2$. What is $h(2)$?

Let $\Diamond(\clubsuit) = 3 \clubsuit^2$. What is $\Diamond(2)$?

Let $g(x) = 3 x^2$. What is $g(\Box)$?

Let $f(x,y) = yx^2$. What is $f(3,2)$?

Let $a(b,c)= c^2+b$. What is $a(3,2)$?

Let $a(b,c)= c^2+b +d$. What is $a(3,2)$?

#### Inequalities

If you allow people to harvest (i.e., catch) a fraction $p$ of the fish in a certain lake each year, then the number of fish in the lake will eventually drop to $1000(1-10p)$. Without worrying about fractional fish, for what range of values of $p$ could this possibly be a reasonable result? Express your answer as an inequality involving $p$.

Let $P=100 p$. What range of $P$ does your above answer correspond to?

Let $s=\beta p$, where $\beta$ (greek letter “beta”) is some fixed number (a parameter). What range of $s$ does your above answer correspond to?

Let $M$ be a positive number (a parameter). If you allow people to harvest (i.e., catch) a fraction $q$ of the fish in a certain lake each year, then the number of fish in the lake will eventually drop to $M(1-10q)$. Without worrying about fractional fish, for what range of values of $q$ could this possibly be a reasonable result? Express your answer as an inequality involving $q$.

Let $k$ and $a$ be positive numbers (parameters). If you allow people to harvest (i.e., catch) a fraction $v$ of the fish in a certain lake each year, then the number of fish in the lake will eventually drop to $k(1-av)$. Without worrying about fractional fish, for what range of values of $v$ could this possibly be a reasonable result? Express your answer as an inequality involving $v$.