0. Functions

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = tan(2x - π)

Express the radius of a sphere as a function of the sphere’s surface area. Then express the surface area as a function of the volume.

State the inputs and outputs of the following relation. Is it a function? {$\left(-3,5\right),\left(0,2\right),\left(3,5\right)$}

State the inputs and outputs of the following relation. Is it a function? {$\left(2,5\right),\left(0,2\right),\left(2,9\right)$}

Find the domain and range of the following graph (write your answer using interval notation).

Test

Decide whether $f$, $g$, or both represent one-to-one functions. <IMAGE>

Daylight function for 40 °N Verify that the function $D(t)=2.8\sin(\frac{2\pi}{365}(t-81))+12$ has the following properties, where t is measured in days and D is the number of hours between sunrise and sunset. It has a period of 365 days.