Questions: Find all points of discontinuity for the function whose graph is shown.

Find all points of discontinuity for the function whose graph is shown.
Transcript text: Find all points of discontinuity for the function whose graph is shown.
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Solution

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Solution Steps

Step 1: Identify the points of discontinuity

Examine the graph to identify where the function is not continuous. Discontinuities can occur where there are breaks, holes, or vertical asymptotes in the graph.

Step 2: Analyze the vertical asymptote

Observe the vertical asymptote at \( x = 0 \). The function approaches infinity as \( x \) approaches 0 from both the left and the right, indicating a discontinuity at \( x = 0 \).

Step 3: Identify the hole in the graph

Notice the hole in the graph at \( x = 1 \). The function is not defined at this point, indicating another discontinuity at \( x = 1 \).

Final Answer

The points of discontinuity for the function are at \( x = 0 \) and \( x = 1 \).

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