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

Explanation:

To determine the truth of the statements, we analyze the graph of the function \(y = f(x)\).

• For statement \(f\), we look at the value of the function at \(x = 1\). From the graph, when \(x=1\), the function value \(f(1)\) is not \(-3\).

Answer:

False