Math Snap

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with three parts - $f(x) = -9$ for $x < -6$
- $f(x) =1$ for $x = -6$
- $f(x) =7x -1$ for $x > -6$
. We are given the points $(-6,-9)$, $(-6,-43)$, $(1,-6)$, $(0,-9)$, $(-5,-36)$, and "None of the above" as possible points on the graph of $f(x)$.

STEP 2

We will check each point by plugging the x-values into the appropriate part of the piecewise function and seeing if we get the corresponding y-value.

STEP 3

First, let's check the point $(-6,-9)$.
For $x=-6$, the function $f(x)$ is defined as $f(x)=1$. So, we should have $f(-6) =1$, not $-9$. So, $(-6,-9)$ is not on the graph of $f(x)$.

STEP 4

Next, let's check the point $(-6,-43)$.
Again, for $x=-6$, the function $f(x)$ is defined as $f(x)=1$. So, we should have $f(-6) =1$, not $-43$. So, $(-6,-43)$ is not on the graph of $f(x)$.

STEP 5

Now, let's check the point $(1,-)$.
For $x=1$, the function $f(x)$ is defined as $f(x)=7x-1$. So, we should have $f(1) =7(1) -1 =$, not $-$. So, $(1,-)$ is not on the graph of $f(x)$.

STEP 6

Next, let's check the point $(0,-9)$.
For $x=0$, the function $f(x)$ is defined as $f(x)=x-1$. So, we should have $f(0) =(0) -1 = -1$, not $-9$. So, $(0,-9)$ is not on the graph of $f(x)$.

Finally, let's check the point $(-5,-36)$.
For $x=-5$, the function $f(x)$ is defined as $f(x)=7x-1$. So, we should have $f(-5) =7(-5) -1 = -36$. So, $(-5,-36)$ is on the graph of $f(x)$.
The point on the graph of $f(x)$ is $(-5,-36)$.