 Sangeetha Pulapaka
1

The function notation to describe the points given, will be f(0) = 3 and f(4) = 6.

This is because a function notation is of the form y = f(x), where x is the input of the function and y is the output.

So when x = 0, y = 3, and when x = 4, y = 6.

Read on if you want to know how to find the equation of the line which runs through the points (0,3) and (4,6)

The equation of the line as you may recall is, in the form y = mx+ c where m is the slope and c is the y-intercept.

We use the slope formula between the two points (0,3) (4,6) to find out the slope of the line, m,

m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{6-3}{4-0} = \frac{3}{4}

Plug in one of the points in the equation to find the y-intercept.

Plug in (0,3) and   m = \frac{3}{4} in y = mx+ c.

to get 3 = \frac{3}{4} \cdot 0 + c

\Rightarrow c = 3

So, the equation of the line is y = \frac{3}{4} x + 3

CHECK:

When x = 0, f(3) = \frac{3}{4} \cdot 0 + 3 = 3

When x = 4, f(4) = \frac{3}{4} \cdot 4 + 3 = 6 Qalaxia QA Bot
0

I found an answer from matheducators.stackexchange.com

How does one explain that transformations 'inside' a function ...

Oct 22, 2014 ... Pictorially you can imagine forming the graph by choosing a large ... When we write "the graph of y=f(x)" we mean "All the points (x,y) ... So (6,5) is on the graph of g. ... In this case "For every point on g there is a corresponding point on f ... Rather, I use a simple function (say, a linear one) and test how it ...

For more information, see How does one explain that transformations 'inside' a function ... Qalaxia Knowlege Bot
0

I found an answer from en.wikipedia.org

Function (mathematics) - Wikipedia

In mathematics, a function is a binary relation between two sets that associates to each element ... For example, the position of a planet is a function of time. ... A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of ... is functional notation, which defines the function using an equation that gives the ...