Section 1
Concepts of functions
Let $f(x)=x^{2}$ and find $f(1), f(2), f(3)$ $f(-1), f(-2)$ and $f(-3)$. What type, one $\rightarrow$ one or many $\rightarrow$ one, of function is $f(x) ?$
Let $f(t)=\frac{9}{5} t+32$. This function converts temperature from ${ }^{\circ} \mathrm{C}$ to ${ }^{\circ} \mathrm{F}$. Evaluate $f(0), f(100)$ and $f(24)$.
Let $g(x)=x^{3}$ and find $g(1), g(-1), g(2)$ $g(-2), g(3)$ and $g(-3)$. What do you notice about your results?
Let $g(t)=-4.9 t^{2}$, and evaluate $g(1), g(\pi)$, $g\left(\frac{1}{\sqrt{4.9}}\right)$
Is $f(h)=\pm \sqrt{20 h}$ a function?If it is a function then is it a one $\rightarrow$ one or a many $\rightarrow$ one function?
[mechanics] The velocity, $v(t)$, of an object is given by$$v(t)=9.8 t$$a Evaluate $v(0), v(1), v(2)$ and $v(5)$.b Find simplified expressions for $v\left(t^{2}\right)$ and $v(t+1)$
[ mechanics] The displacement, $s(t)$, of a particle is given by$$s(t)=t^{3}-t^{2}+5$$
dissipated, $P(V)$, by a resistor is given by$$P(V)=\frac{V^{2}}{R}$$Find $P(I R)$.
$V(R)$, of a battery is given by$$V(R)=\frac{E R}{R+r}$$where $r$ is the internal resistance and $E$ is the electromotive force. Find $V(r)$ and $V(2 r)$.
?? [mechanics] The height, $h(t)$, of an object is given by$$h(t)=200 t-4.9 t^{2}$$a Determine $t$ for $h(t)=0$.b Simplify $h(t+2)$.