I need help finding a function rule.
X Y
-4 -3
-2 0
0 3
So your function rule would be as follows:
(-4,-3), (-2,0), (0,3)
Now use the formula to get the slope
m = (y2-y1)/(x2-x1)
(-4,-3) and (-2,0)
m = (0-(-3))/(-2-(-4))
m= 3/2
m=1.5
so this gives you
y = 1.5x +b
y= 1.5
x = 1
1.5 = 1.5 (1) = b
1.5 = 1.5 +b
b = 0
so your function is
f(x) 1.5x
All I need is a function rule. For example, y= 1/2x + -1
Each increase in x by +2 causes y to increase by +3. Therefore the function is a straight line of the form
y = mx = b and the slope is m = 1.5. Yopu still need to determine the constant term, b.
Use any point such as (x=0, y=3) to get b.
3 = 1.5*0 + b
b = 3
y = 1.5 x + 3
To find a function rule that relates the values of X and Y in the table, we need to look for a pattern or relationship between the two sets of numbers.
Let's focus on the changes in the Y-values as the X-values vary.
When X increases from -4 to -2, Y increases from -3 to 0. This means that for every increase of 2 in X, Y increases by 3.
Similarly, when X increases from -2 to 0, Y increases from 0 to 3. Again, for every increase of 2 in X, Y increases by 3.
Based on this pattern, we can conclude that the relationship between X and Y can be described by the function rule:
Y = 3X + k
To determine the value of k, we can substitute the values of X and Y from any of the given data points in the table into the equation. Let's use the second data point (-2, 0):
0 = 3(-2) + k
0 = -6 + k
Solving for k, we find k = 6.
Therefore, the function rule that relates X and Y is:
Y = 3X + 6