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Homework answers / question archive / Reflect on the concept of function
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
The Learning Journal entry should be a minimum of 400words and not more than 750words.
Answer:
Some examples of the functions are given below.
f (x) = x, f (x) = x2, f (x) = x + 2, f (x) = x3 + 5, etc.
It is possible to view a function.
To draw a graph of a function, calculate the output y-values at different input x-values. Plot the different ordered pairs (x, y) on the graph and draw a curve through them.
Step-by-step explanation
Function: It is relation in which each input has only one output. Basically, it is denoted by f.
Let input is x and output is y, then the output y is called as function of input x. And it is denoted by f (x). i.e. y = f (x)
Some examples of the functions are given below.
f (x) = x, f (x) = x2, f (x) = x + 2, f (x) = x3 + 5, etc.
Here, you can see that each x value has only output. e.g.
For f (x) = x + 2, f (0) = 2, f (1) = 3, f (5) = 7, f (-7) = -5, etc.
In a function, you can never get two or more output on a single input. If you get two or more output on a single input, then that is not a function.
By the use of vertical lines in a graph, you can check that the given graph is a graph of a function or not. On the graph, draw many vertical lines and check, at how many points a vertical line cuts the graph. If any single vertical line cuts the graph at one point, then it is a graph of function, otherwise it is not a graph of function. It means for a function, at one x-value, you have only one y-value.
For y = f (x), the set of input x-values are called the domain of the function and the set of output y-values are called the range of the function.
In your daily life, juicer is a good example of function. For example, if you made one glass mango juice by using juicer, then juicer is your function, mango is input, and mango juice is output. Hence, it is possible to view a function.
To draw a graph of a function, calculate the output y-values at different input x-values. Plot the different ordered pairs (x, y) on the graph and draw a curve through them.
To draw the graph of f (x) = x + 2, calculate the different points.
f (-2) = 0, f (-1) = 1, f (0) = 2, f (1) = 3, f (5) = 7, f (7) = 9
Now, plot the points (-2, 0), (-1, 1), (0, 2), (1, 3), (5, 7), (7, 9) on the graph and draw a line through them to get the graph.
