Question

use the function rule to complete the table.
input (x) output (y)
-1 -3
0
1 ?
2 ?

Explanation:

Step1: Find the function rule

Let's assume the function is linear, so \( y = mx + b \). Using the point \((-1, -3)\) and let's find \( b \) when \( x = 0 \) (the y - intercept). Wait, maybe first check the slope. Let's see, when \( x=-1 \), \( y = - 3 \). Let's assume the function is \( y=2x - 1\)? Wait, no, let's do it properly. Let's suppose the linear function \( y=mx + b \). We know that when \( x=-1 \), \( y=-3 \). Let's find the pattern. Let's check the difference. Wait, maybe the function is \( y = 2x-1\)? No, when \( x = - 1 \), \( 2\times(-1)-1=-3 \), yes! So the function rule is \( y = 2x-1 \).

Step2: Calculate output for \( x = 0 \)

Substitute \( x = 0 \) into \( y = 2x-1 \). So \( y=2\times0 - 1=-1 \).

Step3: Calculate output for \( x = 1 \)

Substitute \( x = 1 \) into \( y = 2x-1 \). So \( y=2\times1 - 1 = 1 \).

Step4: Calculate output for \( x = 2 \)

Substitute \( x = 2 \) into \( y = 2x-1 \). So \( y=2\times2 - 1=3 \).

Answer:

For \( x = 0 \), \( y=-1 \); for \( x = 1 \), \( y = 1 \); for \( x = 2 \), \( y=3 \)

(If we only need to fill the table, the values are: when \( x = 0 \), output is \(-1\); \( x = 1 \), output is \( 1 \); \( x = 2 \), output is \( 3 \))