Journal Unit 1 on functions PDF

Preview

Summary

Review journal question of unit 1 in functions and graphs....

Description

Reflection on Concept of Function

A function is like a machine in which each input produces one output. The input is usually x which is called the independent variable and the output y which is called the dependent variable. Functions are usually written in function notation y=f(x) which shows the relationship between the input and output is a function. For example, our water bill monthly cost is a function of the number of gallons we use. If the cost is 0.30 per gallon and you used 200 gallons for the month. This can be written in a function using our two variables. One variable representing the gallon and other representing monthly cost. The input is normally x = the number of gallon used and the y = the monthly cost. Using this information, we can write a function notation which is used when working in function. Therefore, the function notation would be f(200) = 60x. Each of the function values f(200) = 60x represent a point on a graph. f(200) = 60x would represent the point when x is 200, y is 60. It would also be written as (200.60). In a function a set of inputs is known as the domain, which is x values and a set of outputs is known as the range which is the y values. Each element of the domain should be used only once. If the domain is used more than once the relation is not a function. Domain :Input X

Range: Output y

0

5

1

7

2

9

3

11 Relation is a function

Every element of the range may not be used or paired. The range can also have more than one element paired. For example: Domain :Input X

Range: Output y

0

5

1

7

2

9

3

11 Relation is a function

If one element in the domain produces two outputs, then the relation is not a function. For example: Domain :Input X

Range: Output y

5

0 1 2

7

3

9 Relation is not a function

To understand the concept of function I needed to accommodate the concept of sets, domain, range, relation, function and function notation. The simplest function that I can imagine is f(x)=x or f(x)=x2 .

In my day to day there are many occurring fact that can be interpreted as a function for instance the example I mentioned prior. The consumption of water or the price per gallon of gas we used in our transport to travel every day. In my country a gallon of gas is $13 and I only need 6 gallons to full up my tank. How much would I need to budget for to full the tank. This can be interpreted as a function. You can write an equation y= 13x therefore, using this information you can write a function notation f(x) = 13x (f(6) = 78x). A function can be viewed using an arrow diagram or a graph

Figure showing an arrow diagram in which two sets x and y relate by a function To get the graph of a function you need to determine the domain and range (input and output values). Once the domain and range are determined we draw the graph by placing the domain x values on the x axis and the range y values on the y axis. Using the function y=f(x) plot a point on the graph as (x,y). These points are then joined and will result in different shapes of the graph. The function may be linear, quadratic e.t.c.

Figure showing a straight line (linear)graph from the function...