Which function rule represents the data in the table? X -3, -2, -1, 0, 1. Y -1, 2, 5, 8, 11. How do I find the answer?
( - 3, - 1 ) , ( - 2 , 2 ) , ( - 1 , 5 ) , ( 0 , 8 ) , ( 1, 11 )
Change of x:
- 2 - ( - 3 ) = - 2 + 3 = 1
- 1 - ( - 2 ) = - 1 + 2 = 1
0 - ( - 1 ) = 0 + 1 = 1
1 - 0 = 0
Change of y:
2 - ( - 1 ) = 2 + 1 = 3
5 - 2 = 3
8 - 5 = 3
11 - 8 = 3
When x change 1 y change 3
Slope m = y / x = 3 / 1 = 3
Now straight line equation slope-intercept form:
y = m x + b
where b is y coordinate for x = 0 ( y- intercept)
for x = 0 y = 8
so
y = 3 ∙ 0 + b = 0 + 8 = 8
b = 8
y = m x + b
y = 3 x + 8
Indeed when x change for ∆x = 1 y is change for ∆y = 3
m = ∆y / ∆x = 3 / 1 = 3
To find the function rule that represents the data in the table, we need to examine the relationship between the values of x and y.
Looking at the table, we can observe that for each x value, the y value increases by 3. This indicates that the function has a constant rate of change of 3.
We can also see that when x = -3, y = -1, and when x = 0, y = 8. This suggests that the function has a y-intercept of 8 when x = 0.
Based on this information, we can write the function rule as:
y = 3x + 8
Therefore, the function rule that represents the data in the table is y = 3x + 8.
To find the function rule that represents the data in the table, you need to determine the pattern or relationship between the values of x and y.
Looking at the values in the table, we can see that as x increases by 1, y increases by 3. This suggests a linear relationship between x and y.
To determine the specific function rule, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can choose any two points from the table and use the formula: m = (y₂ - y₁) / (x₂ - x₁).
Let's choose the points (-3, -1) and (-2, 2) from the table to find the slope:
m = (2 - (-1)) / (-2 - (-3))
= (2 + 1) / (-2 + 3)
= 3 / 1
= 3
So the slope (m) is 3.
Next, we need to find the y-intercept (b). We can choose any point from the table and substitute its values into the equation y = mx + b to solve for b.
Let's use the point (0, 8) from the table to find the y-intercept:
8 = 3(0) + b
8 = 0 + b
b = 8
So the y-intercept (b) is 8.
Now we have the slope (m) and the y-intercept (b). Combining them, we can write the function rule: y = 3x + 8.
Therefore, the function rule that represents the data in the table is y = 3x + 8.