Understanding the Linear Function f(x) = x: Graphical Representation and Slope Explanation

f(x)=x

The given function is f(x) = x

The given function is f(x) = x.

This function is a very simple and straightforward linear function with a slope of 1. This means that for every increase or decrease of 1 in the input value (x), the output value (f(x)) also increases or decreases by 1.

To understand this function graphically, you can plot points on a coordinate grid. For example, if we choose some x-values and calculate the corresponding f(x)-values, we can plot those points and connect them to form a straight line.

Let’s take a few values for x and calculate the corresponding f(x)-values:

When x = -3, f(x) = -3
When x = -2, f(x) = -2
When x = -1, f(x) = -1
When x = 0, f(x) = 0
When x = 1, f(x) = 1
When x = 2, f(x) = 2
When x = 3, f(x) = 3

Now, let’s plot these points on a coordinate grid:

(-3, -3) (-2, -2) (-1, -1) (0, 0) (1, 1) (2, 2) (3, 3)

Now, connect these points with a straight line. Since the function is f(x) = x, the line will go through the origin (0,0) and will have a slope of 1.

This means that as you move to the right on the x-axis, the y-coordinate increases by 1, and as you move to the left on the x-axis, the y-coordinate decreases by 1.

Overall, the graphical representation of the function f(x) = x is a straight line that passes through the origin and has a slope of 1.

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