Which function passes through the points (2, 15) and (3, 26)?
A.
y = 11x + 7
B.
y = 11x − 7
C.
y = 7x + 11
D.
y = -11x − 7
E.
y = 7x − 11
Answers
Step-by-step explanation:
There are an infinite number of such functions. It depends on what kind of function you are talking about. Here are two simple functions.
For a linear function: y = ax + b, simply substitute the two points (2, 15) and (3,26).
For (2,15): 15 = 2a + b
For (3,26): 26 = 3a +b
Subtracting the first equation from the second, a = 11.
Substituting into the first equation, 15 = 2(11) + b; 15 = 22 + b; b = -7
f(x) = 11x -7
If you want a quadratic function, you could start with y = a(x^2) + b; Substituting…
For (2,15): 15 = 4a + b
For (3,26): 26 = 9a + b
Subtracting the first equation from the second, 11 = 5a; a = 11/5
Substituting into the first equation: 15 = 4(11/5) + b; 15 -44/5 = b; (75–44)/5 = b; b = 31/5
f(x) = (11/5)x^2 + 31/5
As you see you could endlessly invent polynomial equations that passed through those two points, not to mention other types of functions such as exponential, logarithmic, or trigonometric functions.