Question $y=3 x+1 ;$ domain $=\{-1,0,1\}$

Studdy Solution

STEP 1

What is this asking? We need to find the range of $y$ when $x$ can only be -1, 0, or 1! Watch out! Don't mix up domain and range!
The domain is the set of allowed $x$ values, and the range is the set of $y$ values we get after plugging in the $x$ values.

STEP 2

1. Substitute $x$ values
2. Determine the range

STEP 3

Let's kick things off by plugging in $x = -1$ into our equation: $y = 3 \cdot x + 1$ .
So, $y = 3 \cdot (-1) + 1 = -3 + 1 = -2$ .
When $x$ is -1, $y$ is -2!

STEP 4

Next up, let's tackle $x = 0$ .
Substituting into $y = 3 \cdot x + 1$ , we get $y = 3 \cdot 0 + 1 = 0 + 1 = 1$ .
So, when $x$ is 0, $y$ is 1!

STEP 5

Finally, let's wrap up with $x = 1$ .
Plugging it into $y = 3 \cdot x + 1$ , we have $y = 3 \cdot 1 + 1 = 3 + 1 = 4$ .
When $x$ is 1, $y$ is 4!

STEP 6

We found that when $x$ is -1, $y$ is -2.
When $x$ is 0, $y$ is 1.
And when $x$ is 1, $y$ is 4.

STEP 7

The range is simply all the possible $y$ values.
So, our range is $\{-2, 1, 4\}$ !

STEP 8

The range of the function $y = 3x + 1$ with domain $\{-1, 0, 1\}$ is $\{-2, 1, 4\}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms