Three points on the graph of the function f(x) are {(0,1),(1,4),(2,9)}. Which equation represents f(x) ? f(x)=5x-1 f(x)=4^(x) f(x)=3x+1 f(x)=(x+1)^(2)

Question

Three points on the graph of the function  f(x) are  {(0,1),(1,4),(2,9)}. Which equation represents  f(x) ?  f(x)=5x-1  f(x)=4^(x)  f(x)=3x+1  f(x)=(x+1)^(2)

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Test Option 1: Test the given points with the first option f(x) = 5x - 1. Substitute x = 0 into f(x) = 5x - 1 to see if it equals 1. f(0) = 5(0) - 1 = -1 Since f(0) should equal 1, this option is incorrect.Test Option 2: Test the given points with the second option f(x) = 4^(x). Substitute x = 0 into f(x) = 4^(x) to see if it equals 1. f(0) = 4^(0) = 1 This matches the first point (0,1). Now test the second point (1,4). f(1) = 4^(1) = 4 This matches the second point (1,4). Now test the third point (2,9). f(2) = 4^(2) = 16 Since f(2) should equal 9, this option is incorrect.Test Option 3: Test the given points with the third option f(x) = 3x + 1. Substitute x = 0 into f(x) = 3x + 1 to see if it equals 1. f(0) = 3(0) + 1 = 1 This matches the first point (0,1). Now test the second point (1,4). f(1) = 3(1) + 1 = 4 This matches the second point (1,4). Now test the third point (2,9). f(2) = 3(2) + 1 = 7 Since f(2) should equal 9, this option is incorrect.Test Option 4: Test the given points with the fourth option f(x) = (x + 1)^(2). Substitute x = 0 into f(x) = (x + 1)^(2) to see if it equals 1. f(0) = (0 + 1)^(2) = 1 This matches the first point (0,1). Now test the second point (1,4). f(1) = (1 + 1)^(2) = 4 This matches the second point (1,4). Now test the third point (2,9). f(2) = (2 + 1)^(2) = 9 This matches the third point (2,9). Therefore, this option is correct.

Three points on the graph of the function $f(x)$ are $\{(0,1),(1,4),(2,9)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=5 x-1$ $\newline$ $f(x)=4^{x}$ $\newline$ $f(x)=3 x+1$ $\newline$ $f(x)=(x+1)^{2}$

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