using only the values given in the table for ...
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?\no (-6,-3)\no (-3,-1)\no (-3,0)\no (-6,-5)\n\nx\tf(x)\n-6\t34\n-5\t3\n-4\t-10\n-3\t-11\n-2\t-6\n-1\t-1\n0\t-2\n1\t-15
Answer
# Explanation:
## Step1: Understand increasing - function concept
A function $y = f(x)$ is increasing when as $x$ increases, $f(x)$ also increases.
## Step2: Analyze the table values
For $x=-6$, $f(-6)=34$; for $x = - 5$, $f(-5)=3$. The function is decreasing from $x=-6$ to $x=-5$. For $x=-5$ to $x=-4$, $f(-5) = 3$ and $f(-4)=-10$, it is decreasing. For $x=-4$ to $x=-3$, $f(-4)=-10$ and $f(-3)=-11$, it is decreasing. For $x=-3$ to $x=-2$, $f(-3)=-11$ and $f(-2)=-6$, the function is increasing. For $x=-2$ to $x=-1$, $f(-2)=-6$ and $f(-1)=-1$, the function is increasing. For $x=-1$ to $x = 0$, $f(-1)=-1$ and $f(0)=-2$, it is decreasing. For $x=0$ to $x = 1$, $f(0)=-2$ and $f(1)=-15$, it is decreasing.
## Step3: Determine the increasing interval
The function is increasing for $x$ values in the interval $(-3,-1)$.
# Answer:
$(-3,-1)$