Math Problem Statement
Plot the points on graph
Plot the points on the graph of the function f(x) = |x - 3|.
Solution
To plot the graph of the function , let's break it down step-by-step.
Understanding the Function:
The given function is an absolute value function, which shifts the standard absolute value graph .
- The parent function forms a "V" shape, with the vertex at the origin.
- The function translates this graph horizontally by 3 units to the right. This is because the expression shifts the graph right by 3 units.
Key Points to Plot:
- Vertex: The vertex is at , which is the point where the graph changes direction.
- Other Points: Since the graph is symmetric, choose values for and find the corresponding -values:
- For , . So, is a point.
- For , . So, is a point.
- For , . So, is a point.
- For , . So, is a point.
- For , . So, is a point.
Plot:
- Start by plotting the vertex at .
- Then plot the points , , , , and .
- Connect these points, and remember the graph forms a V-shape with symmetry about the line .
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Math Problem Analysis
Mathematical Concepts
Absolute Value Functions
Graphing Functions
Formulas
f(x) = |x - h| where h shifts the graph horizontally
Theorems
Translation Theorem (Horizontal Shifts in Graphs)
Suitable Grade Level
Grades 8-10