Graphing Absolute Value Functions Warmup 2

• Left 4

• Right 4

• Up 4

• Down 4

Answer explanation

The equation y=|x-4| represents a horizontal shift of the absolute value parent function y=|x|. The '-4' indicates a shift to the right by 4 units. Therefore, the correct transformation is 'Right 4'.

Choose the equation that best matches the graphed function.

Answer explanation

The graph shows a downward-opening V shape, indicating a negative absolute value function. The correct equation is f(x)=-|x|+2, which shifts the vertex up by 2 units.

Answer explanation

The vertex of the function y=|x-3|+1 occurs at the point where the expression inside the absolute value is zero. Setting x-3=0 gives x=3. Substituting x=3 into the function yields y=1. Thus, the vertex is (3,1).

• Shifted left 10

• Shifted right 10

• Shifted up 10

• Shifted down 10

Answer explanation

The equation y=|x|+10 represents a vertical shift of the absolute value parent function. The '+10' indicates that the graph is shifted up by 10 units, making 'Shifted up 10' the correct choice.

• Reflection

• Shifts Up

• Shifts Left

• Rotates 90 degrees

Answer explanation

The equation y=-|x| represents a reflection of the standard V-shaped graph of y=|x| across the x-axis. This transformation flips the graph upside down, making the correct answer 'Reflection'.

• (-16,-11)

• (16,11)

• (16,-11)

• (-16,11)

Answer explanation

The function y=|x+16|-11 has its vertex at the point where the expression inside the absolute value equals zero. Setting x+16=0 gives x=-16. Substituting x=-16 into the function yields y=-11, so the vertex is (-16,-11).