Explain how to write function rule from the table below. Then write a function rule. x=0,2,4,6. y=2,1,0,-1
To write a function rule from a table, we need to identify how the output (y) is related to the input (x). One way to do this is to find the pattern or relationship between the values in each column.
Looking at the table, we can see that as x increases by 2, y decreases by 1. In other words, the rate of change between x and y is -1/2, meaning that for every 2-unit increase in x, y decreases by 1 unit.
Using this information, we can write a function rule in the form y = mx + b, where m is the slope (rate of change) and b is the y-intercept (the value of y when x is 0). To find m, we use the rate of change we identified earlier: m = -1/2. To find b, we can use any point on the line. We'll use the first point (x = 0, y = 2):
y = mx + b
2 = (-1/2)(0) + b
2 = b
So our function rule is:
y = -1/2x + 2
How did you find that 2 was equal to b?
To find the value of b, we need to use the y-intercept of the line, which is the value of y when x is 0. We can use any point on the line to find the value of b, but it is often easiest to use the point where x = 0, since the x-coordinate is already 0 and we only need to find the y-coordinate.
In this case, we use the first point given in the table: x = 0, y = 2. Plugging these values into the equation y = mx + b, we get:
2 = (-1/2)(0) + b
Since multiplying anything by 0 gives 0, the right side of the equation simplifies to:
2 = b
So we have found that the value of b is 2. Therefore, the function rule for the table is:
y = -1/2x + 2
To write a function rule from a table, you need to examine the relationship between the different values of x and y. Let's take a look at the table you provided:
x: 0, 2, 4, 6
y: 2, 1, 0, -1
To find the function rule, you need to determine the pattern between the values of x and y. One way to approach this is to calculate the difference between consecutive x-values and consecutive y-values.
In this case, if we look at the differences between consecutive x-values, we can see that they are all equal to 2. Similarly, the differences between consecutive y-values are all equal to -1.
This suggests that we have a linear relationship where the change in y is a constant multiple of the change in x. In other words, the function rule can be written in the form of y = mx + b, where m represents the slope (the constant multiple) and b represents the y-intercept.
To find the value of m (slope), we can choose any two points from the table and calculate the ratio of the change in y to the change in x. Let's use the first two points, (0, 2) and (2, 1):
m = (change in y) / (change in x)
= (1 - 2) / (2 - 0)
= -1 / 2
= -0.5
Now that we have the slope, we can substitute it into the general form of the function rule and solve for b (y-intercept). Let's use the point (0, 2) again:
2 = -0.5 * 0 + b
2 = b
We found that b = 2, so the function rule for this table is:
y = -0.5x + 2