The ordered pairs represent a function (0,-1). (1,0), (2,3), (3,6), and (4,15)
a. graph the ordered pairs and describe the pattern. Is the function linear or nonlinear?
I said nonlinear.
b. Write an equation that represents the function.
I don't know what the slope would be, what I have right now is
y=?-2
Thank you!
certainly not linear, slopes between pairs of points would have to be the same, --- they are not.
Took differences in the y values up to the fourth difference columns. No constant
so , no polynomial up to 4th degree.
Not even Wolfram found an equation, when to least-fit equations.
http://www.wolframalpha.com/input/?i=equation%7B+(0,-1),+(1,0),+(2,3),+(3,6),++(4,15)%7D
a. To graph the ordered pairs, plot each point on a coordinate plane. Connect the points to see the pattern.
The points (0, -1), (1, 0), (2, 3), (3, 6), and (4, 15) create a curve, not a straight line. The pattern suggests a nonlinear relationship, as the y-values do not increase or decrease at a constant rate. Therefore, you are correct in identifying it as a nonlinear function.
b. To write an equation that represents the function, let's examine the pattern in the y-values. Notice that the difference between consecutive y-values is increasing.
Starting with the first two points, we can find the difference between their y-values:
(1, 0) - (0, -1) = 0 - (-1) = 1.
Now let's find the difference between the next pair of points:
(2, 3) - (1, 0) = 3 - 0 = 3.
Similarly, for the next pair of points:
(3, 6) - (2, 3) = 6 - 3 = 3.
We can observe that the difference is constant at 3 between consecutive y-values. This means that the function has a constant rate of change (slope) between the ordered pairs.
Now, to determine the equation that represents the function, we need to find the equation of a line. Given the constant rate of change and one point on the line, we can use the point-slope form:
y - y1 = m(x - x1),
where (x1, y1) is any point on the line and m is the slope. Let's choose the point (0, -1) from our given ordered pairs.
Plugging in the values, we have:
y - (-1) = 3(x - 0).
Simplifying:
y + 1 = 3x.
Finally, let's rearrange the equation:
y = 3x - 1.
Thus, the equation that represents the function is y = 3x - 1.
a. To graph the ordered pairs, plot the x-values on the x-axis and the corresponding y-values on the y-axis.
Points: (0, -1), (1, 0), (2, 3), (3, 6), (4, 15)
The graph would look like this:
|
|
| x
| x
|x
--------------------
(0,-1) (1,0) (2,3) (3,6) (4,15)
The pattern in the graph is not a straight line. The points do not fall on a straight line, and as the x-values increase, the y-values do not increase or decrease at a constant rate. Therefore, the function is nonlinear.
b. To find the equation that represents the function, you need to determine the relationship between the x and y values.
Looking at the given points, you can observe that as the x-values increase by 1, the y-values do not increase or decrease by a fixed amount. Hence, it is not a linear function.
Without a clear pattern, it is difficult to determine a specific equation for the function from the given information.