Exploring the Linear Parent Function: Graph, Points, and Slope

Graph of Linear Parent Function

The linear parent function is defined as f(x) = x

The linear parent function is defined as f(x) = x. It is the simplest form of a linear function and serves as the basis for all other linear equations.

To graph the linear parent function, we need to plot several points on a coordinate plane and then connect them to form a straight line.

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

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

Now, let’s plot these points on a coordinate plane. The x-values are plotted on the horizontal axis (x-axis), and the corresponding y-values (f(x)) are plotted on the vertical axis (y-axis).

The points we plot are: (0, 0), (1, 1), (2, 2), (-1, -1), and (-2, -2).

After plotting these points, we can connect them with a straight line. Since the linear parent function is represented by a straight line, all the points lie on this line.

The line passes through the origin (0, 0) and has a slope of 1 (meaning it goes up by 1 unit for every 1 unit of horizontal distance). It has a positive slope because the line rises from left to right.

The graph of the linear parent function is a straight line that passes through the origin and has a slope of 1.

Here is an image of the graph:
“`
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-2 | ●
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-1 | ●
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0 | ●
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1 | ●
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2 | ●
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|________________________
-2 -1 0 1 2
“`
Note that this is a simplified version of the linear parent function, and it does not take into account translations, reflections, or scalings that may occur in other linear functions.

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