Question

1. determine if the function shown on the graph is continuous. if not, identify the type (infinite, jump, or removable) and location of discontinuity. continuous discontinuous type: location:

Explanation:

Step1: Recall the definition of a continuous function

A function \( y = f(x) \) is continuous at a point \( x = a \) if \(\lim_{x
ightarrow a}f(x)=f(a)\). A function is continuous on an interval if it is continuous at every point in that interval.

Step2: Analyze the graph

Looking at the graph, there is a hole (a removable discontinuity). A removable discontinuity occurs when \(\lim_{x
ightarrow c}f(x)\) exists, but \(f(c)\) is not defined or \(f(c)
eq\lim_{x
ightarrow c}f(x)\). In this case, the open - circle indicates that the function is not continuous at the point where the open - circle is located.

Answer:

Discontinuous. Type: Removable. Location: The \(x\) - coordinate of the open - circle (assuming from the graph's grid, if we count the squares, say \(x = 5\) (exact value depends on the graph's scale, but the key is it's at the \(x\) - value of the open - circle)).