Questions: Write a piecewise definition for the function and sketch its graph. f(x)=2x+4 if x< f(x)= if x >=

Transcript text: Write a piecewise definition for the function and sketch its graph. \[ f(x)=|2 x+4| \] if $x<$ \[ f(x)= \] if $x \geq$

Solution

Solution Steps

Step 1: Define the piecewise function

The given function is $ f(x) = |2x + 4| $. We need to write its piecewise definition.

For $ x < -2 $: \[ f(x) = -(2x + 4) = -2x - 4 \]

For $ x \geq -2 $: \[ f(x) = 2x + 4 \]

Step 2: Summarize the piecewise function

The piecewise function can be written as: \[ f(x) = \begin{cases} -2x - 4 & \text{if } x < -2 \\ 2x + 4 & \text{if } x \geq -2 \end{cases} \]

Final Answer

\[ f(x) = \begin{cases} -2x - 4 & \text{if } x < -2 \\ 2x + 4 & \text{if } x \geq -2 \end{cases} \]

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -10, "ymax": 10}, "commands": ["y = -2x - 4", "y = 2x + 4"], "latex_expressions": ["$y = -2x - 4$", "$y = 2x + 4$"]}

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