Analyzing the x and its corresponding y, you will realize that the y s are obtained by squaring the x. Hence y⟶x2 You could as well test each of the rules by substituting the value of x into it and see if you will obtain its corresponding y. Testing y⟶x+2 When x=1,y=1+2=3 The result obtained isn't the value in the mapping. The expected value for x=1 is 1. Hence y⟶x+2 is not the rule. Testing y⟶2x When x=1,y⟶2×1=2 The result obtained isn't the value in the mapping. The expected value for x=1 is 1 . Hence y⟶2x is not the rule. Testing y⟶x2 When x=1,y=12=1 When x=2,y=22=4 When x=3,y=32=9 When x=4,y=42=16 When x=5,y=52=25 As you can see, y⟶x2 is the rule as each of the substituted x gave its corresponding y value. You can still verify the last rule. Testing y⟶2x+2 When x=1,y=2(1)+2=4 The result obtained isn't the value in the mapping. The expected value for x=1 is 1. Hence y⟶2x+2 is not the rule.