1) Write the correct function rule that describes the relationship shown in the table below.

X f(x)
1 -1
2
3
4
5

trick:

X f(x) then column of change in f(x)
1 -1
#### 3
2 2
#### 3
3 5 a ha, change in y constant for 1 unit change in x so --- constant slope = 3/1 and form y = 3 x + b
#### 3
4 8
#### 3
5 11
So put in a x and f(x)
like (1,-1)
-1 = 3 (1) + b
b = -4
so
y = 3 x - 4

thanks so much

You are welcome :)

No functional "relationship" is shown, except at x=1. You need to complete the table.

The table is

X f(x)
1 -1
2 2
3 5
4 8
5 11

To determine the correct function rule that describes the relationship shown in the table, we need to look for a pattern.

Looking at the values of x and f(x), we can observe that when x increases by 1, f(x) decreases by 1. This suggests that there might be a linear relationship between x and f(x), with a constant rate of change.

Based on this observation, we can determine that the function rule is likely to be a linear function of the form f(x) = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.

To find the slope value (m), we can choose any two points from the table. Let's select (1, -1) and (2, y), where y is the value of f(x) for x = 2.

By applying the formula for slope: m = (y2 - y1) / (x2 - x1), we can calculate the slope:

m = (y - (-1)) / (2 - 1)
m = (y + 1) / 1
m = y + 1

Since the rate of change is constant, we can see that the slope value is the same as the constant (y + 1).
Now, we need to find the y-intercept (b). Looking at the table, we see that when x = 1, f(x) = -1. This means that -1 is the y-intercept.

Therefore, the function rule that describes the relationship in the table is f(x) = x - 1.