1.1 Function And Change¶

In mathematics, a function is used to represent the dependence of one quantity upon another.

Example¶

In 2015, Boston Massachusetts, had the highest annual snowfall, 110.6 inches, since recording started in 1872. The table shows one 14-day period in which the city broke another record with a total of 64.4 inches.

Daily Snowfall in inches for Boston, January 27 to February 9, 2015 |Day|1|2|3|4|5|6|7|8|9|10|11|12|13|14| |:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:| |Snowfall|22.1|0.2|0|0.7|1.3|0|16.2|0|0|0.8|0|0.9|7.4|14.8|

The snowfall follows a function. Each day, \(t\), has a unique snowfall, \(S\), associated with it.

A function is a rule that takes certain numbers as inputs and assigns to each a definite output number. The set of all input numbers is called the domain of the function and the set of resulting output numbers is called the range of the function.

Quiz #1 Math 2210-12 Calculus 1 James Wibowo¶

Question 1¶

Give Domain and Range for the folded paper volume.¹

a) Domain: \(0< x< 4\) b) Range: \(0\leq V(x) \leq \frac{19- \sqrt{97}}{6}\approx 60\) c) \(h\) Height d) \(V\) Volume

Question 2¶

What is the rule of 4?

Table, Graph, Formula, Words

Question 3¶

What was the numerical approach of the folded paper?¹

A graph.

Question 4¶

What's the formula?

\(V(x)=x(11-2x)(8-2x)\) \(V(x)=4x^3-38x^2+88x\)

Question 5¶

Graph the formula