Question

How do you write linear equations in functional notation?

Answer 1

Hint: Here the solution or answer will be in the descriptive way. We have to explain how the linear equation can be written in the form of functional notation. So we have to know about the linear equation and functional notation and then we transform from linear equation to the functional notation.

Complete step-by-step answer:
Linear equations are equations of the first order. An equation for a straight line is called a linear equation. The general representation of the straight-line equations \[y = mx + b\], where m is the slope of the line and b is the y-intercept. Linear equations are also first-degree equations as it has the highest exponent of variables as 1.
 Example for the linear equation is \[y = 2x + 3\]
Function notation is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation. The most popular function notation is \[f(x)\] which is read "f of x".
Now consider the linear equation
\[y = 3x + 5\]
The above linear equation is just an example.
When we see the linear equation we can notice that the given equation depends on the value of x. Here the value of y depends on the value of x.
So the ‘y’ can be replaced by \[f(x)\]
therefore the given linear equation can be written as
\[f(x) = 3x + 5\]
Hence we have written the linear equation in functional notation.

Note: The functional notation can be written based on the variable which the equation is dependent on the variable. Suppose we have the linear equation \[z = 2t - 2\], then we write the functional notation as \[f(t) = 2t - 2\]. Hence it is any very easy concept.