# Hello! Please, I need a help with this question in my Math assignment: Graph the function defined by: f(x) = -1/2x+3   How can I reach to the points x and y? Do I have to calc the fraction, but I...

Hello! Please, I need a help with this question in my Math assignment:

Graph the function defined by:

f(x) = -1/2x+3

How can I reach to the points x and y? Do I have to calc the fraction, but I can't remember how. Could you help me, please?

quirozd | High School Teacher | (Level 3) Adjunct Educator

Posted on

(This is assuming you meant: `f(x) = -1/2x+3` and not `f(x)=-1/(2x)+3` - message me if I misread your post and I will fix it!)

A function is like a machine that you put in any value, and it spits out a different value based on some expression. For example: f(x) = 2x. When you put in a number (say 3), out pops an answer that is evaluated using the expression 2x. (6 because 2*3 = 6). x is the input, 2x is the output.

In the case of your function: `f(x) = -1/2x+3` , when you plug in (input) an x value, the output is based on the expression `-1/2x+3` . That is handy for getting a few input-output pairs, but how can you represent all of the possible answers? Graph it!

This means that you have to assign an axis to be the input. Most often, this is the horizontal axis (the abscissa or x-axis). The output axis will then be the vertical axis (the ordinate or y-axis). This means that you define y as a function of x or in math: `y=f(x)` .

So you graph `y=-1/2x+3` . But, what kind of graph is it?

Part of algebra is recognizing patterns. This function follows one of those patterns, called the slope-intercept form of a linear function (a straight line) which is `y=mx+b` where `m` is the slope (the rate at which `y` changes with respect to one unit of `x` ) and `b` is the y-intercept (the value of the function when `x` is zero).

Comparing your function to the slope-intercept equation shows that `m=-1/2` and `b=3` .

That means for every one unit of change in the positive x-direction, y changes by `-1/2` units. The graph is a straight line and also has a point at (0,3).

Now we have a mental image of what our graph looks like. A straight line that slopes downward.

Now make a table of input-output values to confirm our mental image.

`x=-4rArrf(-4) = -1/2(-4)+3rArry=5`

hence, we have another point at (-4,5). Repeat for a number of values until you are confident in the shape of the graph (a straight line needs only two points, but it is always good to check at least one more).