Graph h(x)=|-2x|

Problem

h(x)=|−2*x|

Solution

1. Simplify the expression inside the absolute value using the property |a*b|=|a|⋅|b|

h(x)=|−2|⋅|x|

2. Evaluate the absolute value of the constant.

h(x)=2*|x|

3. Identify the parent function and the transformation. The parent function is ƒ(x)=|x| which is a V-shaped graph with a vertex at (0,0) The coefficient 2 represents a vertical stretch by a factor of 2

4. Determine the vertex. Since there are no horizontal or vertical shifts, the vertex remains at (0,0)

5. Calculate points to the right of the vertex (x>0. For x=1 h(1)=2*|1|=2 For x=2 h(2)=2*|2|=4 This creates a ray with a slope of 2

6. Calculate points to the left of the vertex (x<0. For x=−1 h*(−1)=2*|−1|=2 For x=−2 h*(−2)=2*|−2|=4 This creates a ray with a slope of −2

7. Graph the function by plotting the vertex (0,0) and the points (1,2) (2,4) (−1,2) and (−2,4) then connecting them to form a V-shape.

Final Answer

h(x)=2*|x|

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