What is the rule for the function shown in the table?
x: -1 | 0 | 1 | 2
y: -2 | 1 | 4 | 7
A. y= 1/3x + 1
B. y=3x + 1
C. y= 1/3x
D. y= 1/3x + 1
Will someone please help and explain how I can work this out. I have trouble with these.
note that y grows by 3 when x grows by 1. That means you can start with
y = 3x
But since y(0)=1 instead of 3*0=0,
y = 3x+1
you better be right
To determine the rule for the function shown in the table, we need to identify the pattern between the values of x and y.
Let's look at the given values:
x: -1 | 0 | 1 | 2
y: -2 | 1 | 4 | 7
We can observe that as x increases by 1, y increases by 3. This indicates that the function has a constant ratio of change, or a constant slope.
To find the slope, we can choose any two points from the table. Let's select (-1, -2) and (1, 4). The change in y is 4 - (-2) = 6, and the change in x is 1 - (-1) = 2.
Now, we can calculate the slope using the formula:
Slope = (change in y) / (change in x) = 6 / 2 = 3.
So, we have found that the slope of the function is 3.
Now we need to find the y-intercept, which is the value of y when x is 0. From the table, we can see that when x is 0, y is 1.
Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the values, we get:
y = 3x + 1.
Therefore, the correct answer is B. y = 3x + 1.