Given a function whose graph is shown below, under which interval/s is the graph increasing?

A.
(
−
3
,
−
1
)
∪
(
2
,
4
)

B.
(
−
1
,
+
∞
)

C.
(
−
3
,
1
)

D.
(
−
∞
,
−
3
)
∪
(
−
1
,
2
)
∪
(
4
,
+
∞
)

Question

Given a function whose graph is shown below, under which interval/s is the graph increasing?

A. 
(
−
3
,
−
1
)
∪
(
2
,
4
)

B. 
(
−
1
,
+
∞
)

C. 
(
−
3
,
1
)

D. 
(
−
∞
,
−
3
)
∪
(
−
1
,
2
)
∪
(
4
,
+
∞
)

BlackTom AI · Accepted Answer

To determine where the graph is increasing, we look for x-intervals where the function rises as x increases, i.e., where the slope is positive on the plotted curve.

Option A: (-3, -1) ∪ (2, 4)
- On the segment between x = -3 and x = -1, the graph clearly rises from left to right, indicating an increasing interval. Then, from x = 2 to x = 4, the curve again moves upward as x increases, which is another increasing segment. This option matches two distinct rising portions observed on the graph.

Option B: (-1, +∞)
- This claims the function increases from x = -1 all the way to infinity. However, after about x = -1 there is a turning point and the graph does not continuously rise; it has another peak and valleys, indicating portions where the slope becomes negative. Therefore this interval cannot be entirely increasing.

Option C: (-3, 1)
- This would require the entire stretch from -3 to 1 to be increasing. The graph shows at least one local maximum and a subsequent decrease within this range, so the slope changes sign. Hence this interval is not all increasing.

Option D: (-∞, -3) ∪ (-1, 2) ∪ (4, ∞)
- The segment (-∞, -3) does not clearly correspond to an increasing portion based on the given image; the curve there appears to be moving downward as x decreases toward -∞, and the slope is not consistently positive. The middle piece (-1, 2) includes a region where the graph decreases before increasing again, so it is not entirely increasing. The last piece (4, ∞) shows the graph rising, but because the other intervals fail, this composite option does not accurately describe the full set of increasing intervals.

Overall, the only option that aligns with the observed increasing sections on the plotted graph is the combination of the two separate increasing intervals around (-3, -1) and (2, 4), while excluding portions where the graph turns downward or remains flat. The reasoning above examines each interval for consistent positive slope and identifies where such positivity holds or fails across the domain.

SH-GENMATH T-STEM11-O [SA-PT] Assignment 1 Function Definitions and Operations

Given a function whose graph is shown below, under which interval/s is the graph increasing? A. ( − 3 , − 1 ) ∪ ( 2 , 4 ) B. ( − 1 , + ∞ ) C. ( − 3 , 1 ) D. ( − ∞ , − 3 ) ∪ ( − 1 , 2 ) ∪ ( 4 , + ∞ )

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