1. Let's analyze the given sets of points and try to identify if they represent functions. 2. Recall that in a function, each input (x-value) must correspond to exactly one output (y-value). 3. Check each set: - {(2,6), (-3,6), (4,9), (2,10)}: The input 2 maps to 6 and also to 10. This violates the function rule. - {(0,-2), (1,3), (2,3), (3,7)}: All x-values are unique with single y-values, so this is a function. - {(-2,4), (-1,1), (0,0), (1,1)}: All x-values unique, so a function. - {(-2,5), (-1,3), (3,7), (4,12)}: All unique inputs, so a function. - {(-2,4), (-2,6), (0,3), (3,7)}: Input -2 maps to both 4 and 6, so not a function. - {(-2,16), (-1,4), (0,3), (1,4)}: Unique inputs, so a function. - {(1,3), (2,3), (3,3), (4,3)}: Unique inputs, so a function. - {(-4,4), (-3,3), (-2,2), (-1,1), (-4,0)}: Input -4 maps to 4 and 0, not a function. 4. Now let's match functions to their graphs or expressions: - Check the function y = x^2 on points: e.g., (2,6) ? No because 2^2=4 not 6. - y = x^3 at (2,6)? 2^3=8, no. - y = 1/x: at (2,6)? 1/2=0.5, no. - y = |x|: at (-3,6)? |-3|=3, no. - y^2 = 4 - x^2, test (2,6): left side 6^2 =36, right side 4-4=0, no. - y = ±√(1 - 2x), test (0,-2): y=±√(1-0)=±1, no -2. - x/(x+2), test (1,3): 1/3=0.333, no. - x/(3x - 1), test (1,3): 1/(3*1-1)=1/2=0.5, no. - x + y^2 = 1, test (0,-2): 0 + 4 = 4, not 1. - y=2x^2 - 3x + 4 at (2,6): 2*4 - 6 + 4 =8 - 6 + 4 =6, yes. - 2x^2 + 3y^2 =1, test (0,3): left 0+27=27 not 1. - x^2 - 4y^2=1 at (1,3): 1 - 36= -35 not 1. 5. For the given function points, the functions can be verified similarly, typically these are standard functions or rational functions. 6. The message is primarily about understanding the definition of a function with sets of points. Final conclusion: The sets with repeated x-values mapping to different y-values are not functions. "q_count":8