the graph below is the function y = f(x)\ny = f(x)\nf(3)=____\nlim(x→2) f(x)=____\nlim(x→4)…

Explanation:

Step1: Find f(3)

From the graph, when (x = 3), the solid - dot value of the function is (1), so (f(3)=1).

Step2: Find (\lim_{x\rightarrow2}f(x))

As (x) approaches (2) from both the left - hand side and the right - hand side, the function values approach (3). So (\lim_{x\rightarrow2}f(x)=3).

Step3: Find (\lim_{x\rightarrow4}f(x))

The left - hand limit (\lim_{x\rightarrow4^{-}}f(x)=2) and the right - hand limit (\lim_{x\rightarrow4^{+}}f(x)=3). Since the left - hand limit and the right - hand limit are not equal, (\lim_{x\rightarrow4}f(x)) does not exist.

Step4: Find (\lim_{x\rightarrow4^{+}}f(x))

As (x) approaches (4) from the right - hand side, the function values approach (3). So (\lim_{x\rightarrow4^{+}}f(x)=3).

Step5: Find (\lim_{x\rightarrow4^{-}}f(x))

As (x) approaches (4) from the left - hand side, the function values approach (2). So (\lim_{x\rightarrow4^{-}}f(x)=2).

Step6: Find (\lim_{x\rightarrow1}f(x + 2))

Let (t=x + 2). When (x\rightarrow1), (t\rightarrow3). Then (\lim_{x\rightarrow1}f(x + 2)=\lim_{t\rightarrow3}f(t)). From the graph, (\lim_{t\rightarrow3}f(t)=1).

Answer:

(f(3)=1) (\lim_{x\rightarrow2}f(x)=3) (\lim_{x\rightarrow4}f(x)) does not exist (\lim_{x\rightarrow4^{+}}f(x)=3) (\lim_{x\rightarrow4^{-}}f(x)=2) (\lim_{x\rightarrow1}f(x + 2)=1)