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Graph g(x)=5|x-6|+2.

Graph g(x)=5∣x−6∣+2 g(x)=5|x-6|+2 .

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Transformations of absolute value functions: translations, reflections, and dilationsright chevron icon

Full solution

Q. Graph g(x)=5∣x−6∣+2 g(x)=5|x-6|+2 .
  1. Understand Basic Shape: First, let's understand the basic shape of the graph of y=∣x∣y = |x|. It's a V-shaped graph that opens upwards with the vertex at the origin (0,0)(0,0).
  2. Analyzing Function: Now, let's look at our function g(x)=5∣x−6∣+2g(x) = 5|x - 6| + 2. The ＂∣x−6∣|x - 6|＂ part shifts the vertex of the V to the right by 66 units, so the new vertex is at (6,2)(6,2).
  3. Vertical Stretch: The ＂55＂ in front of the absolute value means we stretch the graph vertically by a factor of 55. This makes the V-shape steeper.
  4. Final Shift: Lastly, the ＂+2+ 2＂ at the end of the function moves the entire graph up by 22 units. But wait, we already accounted for this when we placed the vertex at (6,2)(6,2). So, no further shifting is needed.

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