Question

which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are false?
a. the statement ( lim_{x \to 2} f(x) ) does not exist is false.
b. the statement ( lim_{x \to 2} f(x) = 2 ) is false.
c. the statement ( lim_{x \to 1} f(x) ) does not exist is true.
d. the statement ( lim_{x \to c} f(x) ) exists at every point ( c ) in ( (-1,1) ) is true.
e. the statement ( lim_{x \to c} f(x) ) exists at every point ( c ) in ( (1,3) ) is true.
f. the statement ( f(1) = - 3 ) is false.
g. the statement ( f(1) = 0 ) is

Explanation:

Step1: Analyze the function at \(x = 1\)

Looking at the graph, when \(x = 1\), the function value \(f(1)\) is the \(y\)-coordinate of the point on the graph at \(x = 1\). From the graph, we can see that \(f(1)=0\).

Answer:

The statement \(f(1) = 0\) is true.