The graph will have a V-shape with the vertex at the point (2,0) where there is a hole. The arms of the V will extend upwards to the left of x=2 and downwards to the right of x=2.
The graph of the function f(x)=−∣x−2∣ can be understood by breaking it down into different intervals based on the expression inside the absolute value.
When x<2: In this interval, ∣x−2∣ is negative, so −∣x−2∣ is positive.
The function is equal to its positive counterpart ∣x−2∣ with a negative sign.
As x moves to the left of 2, the graph reflects across the y-axis, resulting in the same shape as
f(x)=∣x−2∣ but flipped upside down.
When x=2: At x=2, ∣x−2∣ becomes zero, and −∣x−2∣ is also zero.
Therefore, there is a point of discontinuity or a hole in the graph at x=2.
When x>2: In this interval, ∣x−2∣ is positive, so −∣x−2∣ is negative.
The graph is the reflection of f(x)=∣x−2∣ below the x-axis.
Therefore, he graph will have a V-shape with the vertex at the point
(2,0) where there is a hole. The arms of the V will extend upwards to the left of x=2 and downwards to the right of x=2.
Question
Draw the graph of function f(x)=-|x-2|