Math Snap

STEP 1

What is this asking?
Which of these points don't live on the graph of the function $f(x) = \frac{1 - x^2}{x}$?
Watch out!
Make sure to plug in the x-value into the function and see if it spits out the y-value!
Don't mix them up!

STEP 2

1. Test point (1, 0)
2. Test point (0, 1)
3. Test point (-2, 3/2)
4. Test point (-1, 0)
5. Test point (-3, -10/3)

STEP 3

Alright, let's plug in $x = 1$ into our function! $f(1) = \frac{1 - (1)^2}{1} = \frac{1 - 1}{1} = \frac{0}{1} = 0$.
Boom! This matches the y-value of 0, so the point $(1, 0)$ is on the graph.

STEP 4

Now, let's try $x = 0$. $f(0) = \frac{1 - (0)^2}{0} = \frac{1}{0}$.
Uh oh!
We can't divide by zero!
This means the function isn't defined at $x = 0$, so the point $(0, 1)$ is not on the graph.

STEP 5

Let's substitute $x = -2$. $f(-2) = \frac{1 - (-2)^2}{-2} = \frac{1 - 4}{-2} = \frac{-3}{-2} = \frac{3}{2}$.
This matches the y-value of $\frac{\textbf{3}}{\textbf{2}}$, so $(-2, \frac{3}{2})$ is on the graph!

STEP 6

Time for $x = -1$! $f(-1) = \frac{1 - (-1)^2}{-1} = \frac{1 - 1}{-1} = \frac{0}{-1} = 0$.
This matches the y-value of 0, so $(-1, 0)$ is on the graph.

STEP 7

Lastly, let's check $x = -3$. $f(-3) = \frac{1 - (-3)^2}{-3} = \frac{1 - 9}{-3} = \frac{-8}{-3} = \frac{8}{3}$.
This doesn't match the y-value of $-\frac{\textbf{10}}{\textbf{3}}$, so $(-3, -\frac{10}{3})$ is not on the graph.

The points that don't belong to the graph are $(0, 1)$ and $(-3, -\frac{10}{3})$.