Graph f(x)=|2x+4|

Problem

ƒ(x)=|2*x+4|

Solution

1. Identify the parent function as the absolute value function y=|x| which has a characteristic "V" shape.

2. Find the vertex by setting the expression inside the absolute value to zero: 2*x+4=0⇒2*x=−4⇒x=−2

3. Calculate the y-coordinate of the vertex by substituting x=−2 into the function: ƒ*(−2)=|2*(−2)+4|=0 The vertex is at (−2,0)

4. Determine the y-intercept by evaluating the function at x=0 ƒ(0)=|2*(0)+4|=4 The y-intercept is at (0,4)

5. Find additional points to define the slopes of the two branches. For x=−3 ƒ*(−3)=|2*(−3)+4|=|−2|=2 For x=−1 ƒ*(−1)=|2*(−1)+4|=|2|=2

6. Plot the points (−2,0) (0,4) (−3,2) and (−1,2) and draw two rays originating from the vertex (−2,0) passing through these points.

Final Answer

ƒ(x)=|2*x+4|

The graph is a V-shaped function with a vertex at (−2,0) a y-intercept at (0,4) and slopes of 2 and −2 for the right and left branches respectively.

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