Question

Which sets of ordered pairs are from linear functions? Select the TWO answers that apply. Group of answer choices {(0,1),(1,2),(2,3),(3,4)} {(0,0),(1,1),(2,4),(3,9)} {(1,1),(2,8),(3,27),(4,64)} {(0,4),(1,6),(3,10),(5,14)}

Answer 1

• {(0,1),(1,2),(2,3),(3,4)}
• {(0,4),(1,6),(3,10),(5,14)}

Explanation:

When x-differences are the same, y-differences will be the same for a linear function. When they are not the same, they will be proportional for a linear function.

{(0,1),(1,2),(2,3),(3,4)} - x-differences are all the same; y-differences are all 1 (linear, y=x+1)

{(0,0),(1,1),(2,4),(3,9)} - x-differences are all the same; y-differences increase (this is a quadratic function: y=x^2)

{(1,1),(2,8),(3,27),(4,64)} - x-differences are all the same; y-differences increase (this is a cubic function: y=x^3)

{(0,4),(1,6),(3,10),(5,14)} - x-differences are 1, 2, 2; y-differences are 2, 4, 4, so are proportional to (double) the x-differences (linear; y=2x+4)