Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)
Answers
Answer:
To know if a function is increasing or decreasing in a given interval [a,b], we will apply the following formula
\frac{f(b)-f(a)}{b-a}
b−a
f(b)−f(a)
If the value is positive, then the function is increasing
If the value is negative, then the function is decreasing
case A) (-6,-3)(−6,−3)
see in the table
\begin{lgathered}f(-6)=34\\f(-3)=-11\end{lgathered}
f(−6)=34
f(−3)=−11
substitute in the formula above
\frac{-11-34}{-3+6}
−3+6
−11−34
\frac{-45}{3}
3
−45
-15−15 -------> is negative
therefore
In the interval (-6,-3)(−6,−3) the function is decreasing
case B) (-3,-1)(−3,−1)
see in the table
\begin{lgathered}f(-3)=-11\\f(-1)=-1\end{lgathered}
f(−3)=−11
f(−1)=−1
substitute in the formula above
\frac{-1+11}{-1+3}
−1+3
−1+11
\frac{10}{2}
2
10
55 -------> is positive
therefore
In the interval (-3,-1)(−3,−1) the function is increasing
case C) (-3,0)(−3,0)
see in the table
\begin{lgathered}f(-3)=-11\\f(0)=-2\end{lgathered}
f(−3)=−11
f(0)=−2
substitute in the formula above
\frac{-2+11}{0+3}
0+3
−2+11
\frac{9}{3}
3
9
33 -------> is positive
therefore
In the interval (-3,0)(−3,0) the function is increasing
case D) (-6,-5)(−6,−5)
see in the table
\begin{lgathered}f(-6)=34\\f(-5)=3\end{lgathered}
f(−6)=34
f(−5)=3
substitute in the formula above
\frac{3-34}{-5+6}
−5+6
3−34
\frac{-31}{1}
1
−31
-31−31 -------> is negativeUsing only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)
therefore
In the interval (-6,-5)(−6,−5) the function i
Answer:
It's (–3, –1)
Explanation: