directions: the graph of the rational function f is shown above. use the graph of f to answer problems 4 - 7.
4. $ \lim _ { x \
ightarrow 2 ^ { + } } f ( x ) = $
(a) 2
(b) 3
(c) $ - \infty $
(d) $ \infty $
5. $ \lim _ { x \
ightarrow 2 ^ { - } } f ( x ) = $
(a) 2
(b) 3
(c) $ - \infty $
(d) $ \infty $
6. $ \lim _ { x \
ightarrow \infty } f ( x ) = $
(a) 2
(b) 3
(c) $ - \infty $
(d) $ \infty $
7. on the interval $ ( 3, \infty ) $, the graph of f is
(a) decreasing at a decreasing rate.
(b) decreasing at an increasing rate.
(c) increasing at a decreasing rate.
(d) increasing at an increasing rate.

Question

Accepted Answer

### Question 4
# Explanation:
## Step1: Analyze the right - hand limit as $x\to2^{+}$
Looking at the graph, as $x$ approaches $2$ from the right ($x = 2^{+}$), the function values go to $-\infty$.

# Answer:
C. $-\infty$

### Question 5
# Explanation:
## Step1: Analyze the limit as $x\to-\infty$
As $x$ approaches $-\infty$, the graph of the function approaches the horizontal asymptote $y = 3$.

# Answer:
B. $3$

### Question 6
# Explanation:
## Step1: Analyze the left - hand limit as $x\to2^{-}$
Looking at the graph, as $x$ approaches $2$ from the left ($x = 2^{-}$), the function values go to $\infty$.

# Answer:
D. $\infty$

### Question 7
# Explanation:
## Step1: Analyze the slope and concavity on $(3,\infty)$
On the interval $(3,\infty)$, the function is increasing (since $y$ - values are getting larger as $x$ increases). The slope of the tangent line to the graph is positive but getting smaller (the function is “flattening out”). So, the function is increasing at a decreasing rate.

# Answer:
C. increasing at a decreasing rate.

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QUESTION IMAGE

Question

Explanation:

Question 4

Step1: Analyze the right - hand limit as \(x\to2^{+}\)

Step1: Analyze the limit as \(x\to-\infty\)

Step1: Analyze the left - hand limit as \(x\to2^{-}\)

Answer:

Question 5