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Draw the graph of f(x)=[[x - 4]] - 2

User Dapug
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1 Answer

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Answer:

See attachment.

Explanation:

Given absolute value function:


f(x)=|x-4|-2

The parent absolute value function is f(x) = |x|.

Graph of the parent absolute value function:

  • Vertex at (0, 0)
  • |y| = -x if x ≤ 0
  • |y| = x if x ≥ 0

Translations


\textsf{For $a > 0$}:


f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.


f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.


f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.


f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.

The graph of the given function is a transformation of the parent function by:

  • Translation of 4 units right.
  • Translation of 2 units down.

Therefore, the vertex of the given function is (4, -2).

Find two further points on the graph by inputting x-values either side of the x-value of the vertex into the given function:


\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}


\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}

To draw the graph of the given function:

  • Plot the vertex (4, -2).
  • Draw a straight line from the vertex through point (8, 2).
  • Draw a straight line from the vertex through point (0, 2).
Draw the graph of f(x)=[[x - 4]] - 2-example-1
User James Black
by
8.0k points

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