Graph this function:
y=|x–3|
Click to plot the vertex first.

The function \( y = |x - 3| \) is an absolute value function. The vertex of this function is at the point where the expression inside the absolute value is zero. 

To find the vertex, set \( x - 3 = 0 \):
\[ x - 3 = 0 \]
\[ x = 3 \]

At \( x = 3 \), \( y = |3 - 3| = 0 \). So, the vertex is at the point (3, 0).

Let's start by plotting the vertex on the graph.

Next, to understand the shape of the graph:
- For \( x \geq 3 \), \( y = x - 3 \) (the function behaves like a linear function with slope 1).
- For \( x < 3 \), \( y = 3 - x \) (the function behaves like a linear function with slope -1).

The graph of \( y = |x - 3| \) forms a "V" shape with the vertex at (3, 0).

Would you like a visual graph of this function? If so, I can create one for you.

Graph this function: y=|x–3| Click to plot the vertex first.

Learn how to graph the absolute value function y = |x - 3|. This problem explains how to find the vertex of the function and understand its V-shaped graph. The solution covers algebraic concepts like graphing piecewise linear functions and working with absolute value equations. Suitable for students in Grades 8-10.

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