Question

d) $f(1)=$
e) $lim_{x
ightarrow2}f(x)=$
f) $lim_{x
ightarrow - 2^{+}}f(x)=$
g) $lim_{x
ightarrow - 2^{-}}f(x)=$
h) $f(-2)=$
a) 2
b) dne
c) 4
d) 3
e) 2
f) dne
g)

Explanation:

Since the function \(f(x)\) is not given, we cannot provide a step - by - step solution for calculating the function values and limits. However, if we assume we have the graph or the formula of the function \(f(x)\):

d) \(f(1)\)

To find \(f(1)\), we substitute \(x = 1\) into the function \(f(x)\). If we know the formula of \(f(x)\), we just calculate the value. If we have the graph of \(y=f(x)\), we find the \(y\) - value corresponding to \(x = 1\) on the graph.

e) \(\lim_{x

ightarrow2}f(x)\)
The limit \(\lim_{x
ightarrow2}f(x)\) exists if and only if \(\lim_{x
ightarrow2^{-}}f(x)=\lim_{x
ightarrow2^{+}}f(x)\). We need to find the left - hand limit (values of \(f(x)\) as \(x\) approaches \(2\) from the left, \(x<2\)) and the right - hand limit (values of \(f(x)\) as \(x\) approaches \(2\) from the right, \(x > 2\)). If these two one - sided limits are equal, then \(\lim_{x
ightarrow2}f(x)\) is equal to that common value.

f) \(\lim_{x

ightarrow - 2^{+}}f(x)\)
We consider the values of \(f(x)\) as \(x\) approaches \(-2\) from the right (\(x>-2\)). We look at the behavior of the function for values of \(x\) that are slightly greater than \(-2\).

g) \(\lim_{x

ightarrow - 2^{-}}f(x)\)
We consider the values of \(f(x)\) as \(x\) approaches \(-2\) from the left (\(x < - 2\)). We look at the behavior of the function for values of \(x\) that are slightly less than \(-2\).

h) \(f(-2)\)

To find \(f(-2)\), we substitute \(x=-2\) into the function \(f(x)\). If we know the formula of \(f(x)\), we calculate the value. If we have the graph of \(y = f(x)\), we find the \(y\) - value corresponding to \(x=-2\) on the graph.

Since the function \(f(x)\) is not given, we cannot give numerical answers. But if we assume we have all the necessary information about \(f(x)\):

Step1: For \(f(1)\)

Substitute \(x = 1\) into \(f(x)\) (if formula known) or read from graph.

Step2: For \(\lim_{x

ightarrow2}f(x)\)
Check if \(\lim_{x
ightarrow2^{-}}f(x)=\lim_{x
ightarrow2^{+}}f(x)\)

Step3: For \(\lim_{x

ightarrow - 2^{+}}f(x)\)
Examine values of \(f(x)\) for \(x>-2\) approaching \(-2\)

Step4: For \(\lim_{x

ightarrow - 2^{-}}f(x)\)
Examine values of \(f(x)\) for \(x < - 2\) approaching \(-2\)

Step5: For \(f(-2)\)

Substitute \(x=-2\) into \(f(x)\) (if formula known) or read from graph

Since we don't have the function \(f(x)\), we can't provide a final answer. If we assume the given options are correct based on some un - shown function:

Answer:

d) \(f(1)=3\)
e) \(\lim_{x
ightarrow2}f(x)=2\)
f) \(\lim_{x
ightarrow - 2^{+}}f(x)=\text{DNE}\)
g) (No answer given in options for this part in the provided image)
h) (No answer given in options for this part in the provided image)