Question

The graph of a function f is given. which of the following statement about f is true.

Answer 1

The options we have are:

A)

`\begin{gathered} \lim _(x\to0)f(x)=1 \\ \end{gathered}`

B)

`\lim _(x\to0^-)f(x)=2`

C)

`\lim _(x\to2^-)f(x)=1`

D)

`\lim _(x\to2)f(x)=3`

To solve this limits problem we need to consider the graph and our options.

It is important to note the minus sign on some of the options because the sign on the number that x tends to indicates the direction from where f(x) comes from.

We discard option A because f(x) only lends to 1, when x=0 from the left, so for this to be righ the x-->0 must have a "-" on the zero. (This is because the - represents that it tends to zero from the left)

We discard option B, because when x--->0- (which can read as: x tends to zero from the left) the value of f(x) tends to 1, not 2 as option B states.

Option C indicates that when x tends to 2 from the left (x-->2-) the value of f(x) is 1. This option is right. Because as we can see in the graph:

Answer: C