Questions: Does the absolute value graph below flip or not flip? Support your answer. f(x)=2x-9+3

Solution Steps

The general form of an absolute value function is: \[ f(x) = a|x - h| + k \] where:

• \( a \) determines the vertical stretch or compression and whether the graph flips.
• \( h \) determines the horizontal shift.
• \( k \) determines the vertical shift.

The given function is: \[ f(x) = 2|x - 9| + 3 \] Comparing this to the general form, we identify:

• \( a = 2 \)
• \( h = 9 \)
• \( k = 3 \)

The graph of an absolute value function flips (opens downward) if \( a \) is negative. In this case, \( a = 2 \), which is positive. Therefore, the graph does not flip.

Final Answer