Question

The graph of y = f(x) is the solid black graph below. Which function represents the dotted

graph?
Answer

Y=f(x-1)+1
Y=f(x+1)-1
Y=f(x+1)+1
Y=f(x-1)-1

Answer 1

The function represented by the dotted graph is y = |x +1| - 1.

The graph of an absolute function

The graph of an absolute value function expressed as f(x) = |x| has a V-shape structure when show on a graph. The absolute value function shows the distance of a number from zero on the line, as a result it's always non-negative.

The shape of the graph can either open:

• Upward if f(x) = |x|
• Downward if f(x) = -|x|

From the given graph, the parent function of the graph y = |x|. Now, the graph is shifted to the left by 1 unit, we have y = |x+1|, and downward by 1 unit i.e. y = |x +1| - 1.

Therefore, the function represented by the dotted graph is y = |x +1| - 1.