Questions: Which statement is true about the given function? f(x)<0 over the intervals (-โˆž,-2.7) and (0.8, โˆž). f(x)<0 over the intervals (-โˆž,-2.7) and (-1,0.8). f(x)>0 over the intervals (-โˆž,-2.7) and (-1,0.8). f(x)>0 over the intervals (-โˆž,-1) and (0.8, โˆž).

Which statement is true about the given function?
f(x)<0 over the intervals (-โˆž,-2.7) and (0.8, โˆž).
f(x)<0 over the intervals (-โˆž,-2.7) and (-1,0.8).
f(x)>0 over the intervals (-โˆž,-2.7) and (-1,0.8).
f(x)>0 over the intervals (-โˆž,-1) and (0.8, โˆž).
Transcript text: Which statement is true about the given function? $f(x)<0$ over the intervals $(-\infty,-2.7)$ and $(0.8, \infty)$. $f(x)<0$ over the intervals $(-\infty,-2.7)$ and $(-1,0.8)$. $f(x)>0$ over the intervals $(-\infty,-2.7)$ and $(-1,0.8)$. $f(x)>0$ over the intervals $(-\infty,-1)$ and $(0.8, \infty)$.
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Solution

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Solution Steps

Step 1: Analyze the graph

We are looking for the intervals where f(x) is negative (i.e., below the x-axis).

Step 2: Identify intervals where f(x) < 0

The graph is below the x-axis roughly between x = -โˆž and x = -2.7, and also between x = -1 and x = 0.8.

Step 3: Match with the given options

The correct statement is ๐‘“(๐‘ฅ) < 0 over the intervals (โˆ’โˆž,โˆ’2.7) and (โˆ’1,0.8).

Final Answer

$f(x)<0$ over the intervals $(-\infty,-2.7)$ and $(-1,0.8)$.

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