Plot the ordered pairs (-1,11), (2,-1), (4,21) on the coordinate plane. Which of the following functions goes through the three given points?𝑎)𝑓(𝑥)=3𝑥2−7𝑥+1𝑏)𝑓(𝑥)=2𝑥2+𝑥+2𝑐)𝑓(𝑥)=−𝑥+3Group of answer choices𝑐)𝑓(𝑥)=−𝑥+3

To determine which function goes through the three given points, we need to substitute the x and y values of each point into the functions and see which one holds true for all three points.

Let's start with function a) 𝑓(𝑥)=3𝑥²−7𝑥+1

For point (-1,11), substituting x = -1 into the function gives: f(-1) = 3*(-1)² - 7*(-1) + 1 = 3 + 7 + 1 = 11, which matches the y value of the point.

For point (2,-1), substituting x = 2 into the function gives: f(2) = 3*(2)² - 7*2 + 1 = 12 - 14 + 1 = -1, which matches the y value of the point.

For point (4,21), substituting x = 4 into the function gives: f(4) = 3*(4)² - 7*4 + 1 = 48 - 28 + 1 = 21, which matches the y value of the point.

So, function a) 𝑓(𝑥)=3𝑥²−7𝑥+1 goes through all three points.

We can stop here since the question asks for which of the following functions goes through the three given points, and we have found one. However, if you want to be thorough, you can check the other two functions in the same way.