Which function contains this set of ordered pairs?
{(–2, –7), (0, 1), ( 3, –17)}
all kinds of functions.
Any 3 non-collinear points can be expressed by a quadratic, a cubic, a trig function ....
e.g Wolfram found:
y = -4.7632sinx + 8.70749cosx - 7.70749
if you want a quadratic"
y = ax^2 + bx + c
-7 = 4a - 2b + c
1 = c
-17 = 9a + 3b + c
solve for a, b, and c
To determine which function contains a given set of ordered pairs, we need to examine the pattern or relationship between the x-values and the corresponding y-values.
Let's take a look at the given set of ordered pairs: {(–2, –7), (0, 1), (3, –17)}.
We can start by looking at the x-values (–2, 0, 3) and the corresponding y-values (–7, 1, –17).
To determine if there is a pattern, let's calculate the differences between consecutive x-values and the differences between consecutive y-values:
Difference between consecutive x-values:
0 - (-2) = 2
3 - 0 = 3
Difference between consecutive y-values:
1 - (-7) = 8
(-17) - 1 = -18
If there is a linear relationship, the differences between consecutive y-values should be proportional to the differences between consecutive x-values. Let's check if this is the case:
Differences in y-values: 8 and -18
Differences in x-values: 2 and 3
To check proportionality, we can divide the differences in y-values by the differences in x-values:
8 ÷ 2 = 4
-18 ÷ 3 = -6
Since the quotients are not equal (4 ≠ -6), we can conclude that the given set of ordered pairs does not represent a linear function.
In this case, we would need more information in order to determine the specific type of function (such as quadratic, exponential, etc.) that contains this set of ordered pairs.