How do you write the rule for a function
with the table
x=0,2,4,5
y=4,6,8,9
?
hint:
y=x+__?
4=0+__
6=2+__
8=4+__
9=5+__
So what would it be? I'm so confused
what would you add to 0 to get 4?
what would you add to 2 to get 6?
etc.
y=x+__
in other words, what would you add to x to get y?
4.. so it'd be 4
To write the rule for a function given a table of x and y values, you need to identify the pattern or relationship between the x and y values. Let's look at the given table:
x: 0, 2, 4, 5
y: 4, 6, 8, 9
To find the rule, we need to examine how the y values change as the x values change.
From the table, we can observe that as x increases by 2 (from 0 to 2, and from 2 to 4), y increases by 2 as well. However, when x increases by 1 (from 4 to 5), y only increases by 1.
Based on this pattern, we can write the rule as:
y = 2x + c
To determine the constant term 'c', we can plug in one of the given x and y values into the equation. Let's use the first pair: x = 0, y = 4:
4 = 2(0) + c
4 = 0 + c
c = 4
Therefore, the rule for the function is y = 2x + 4.