Questions: Which statement is true about the given function?
f(x)<0 over the intervals (-â,-2.7) and (0.8, â).
f(x)<0 over the intervals (-â,-2.7) and (-1,0.8).
f(x)>0 over the intervals (-â,-2.7) and (-1,0.8).
f(x)>0 over the intervals (-â,-1) and (0.8, â).
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 $(0.8, \infty)$.
Solution
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 = -â and x = -2.7, and also between x = -1 and x = 0.8.
Step 3: Match with the given options
The correct statement is đ(đĨ) < 0 over the intervals (ââ,â2.7) and (â1,0.8).
Final Answer
$f(x)<0$ over the intervals $(-\infty,-2.7)$ and $(-1,0.8)$.