Three points on the graph of the function f(x) are {(0,5),(1,6),(2,9)}. Which equation represents f(x) ? f(x)=x^(2)+5 f(x)=x+5 f(x)=5*((6)/(5))^(x) f(x)=3x+3

Question

Three points on the graph of the function  f(x) are  {(0,5),(1,6),(2,9)}. Which equation represents  f(x) ?  f(x)=x^(2)+5  f(x)=x+5  f(x)=5*((6)/(5))^(x)  f(x)=3x+3

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Substitution Testing: To determine which equation represents the function f(x), we will substitute each given point into each of the proposed equations and check for consistency.Point (0,5): First, let's test the point (0,5) in each equation. For f(x) = x^2 + 5, when x = 0, f(0) = 0^2 + 5 = 5. For f(x) = x + 5, when x = 0, f(0) = 0 + 5 = 5. For f(x) = 5 * (6/5)^x, when x = 0, f(0) = 5 * (6/5)^0 = 5 * 1 = 5. For f(x) = 3x + 3, when x = 0, f(0) = 3*0 + 3 = 3. The first three equations are consistent with the point (0,5), but the last one is not.Point (1,6): Next, let's test the point (1,6) in the remaining equations. For f(x) = x^2 + 5, when x = 1, f(1) = 1^2 + 5 = 6. For f(x) = x + 5, when x = 1, f(1) = 1 + 5 = 6. For f(x) = 5 * (6/5)^x, when x = 1, f(1) = 5 * (6/5)^1 = 5 * 6/5 = 6. All three equations are consistent with the point (1,6).Point (2,9): Finally, let's test the point (2,9) in the remaining equations. For f(x) = x^2 + 5, when x = 2, f(2) = 2^2 + 5 = 4 + 5 = 9. For f(x) = x + 5, when x = 2, f(2) = 2 + 5 = 7. For f(x) = 5 * (6/5)^x, when x = 2, f(2) = 5 * (6/5)^2 = 5 * 36/25 = 5 * 1.44 = 7.2. Only the first equation, f(x) = x^2 + 5, is consistent with the point (2,9).Final Equation Determination: Since only the equation f(x) = x^2 + 5 is consistent with all three given points, this is the equation that represents the function f(x).

Three points on the graph of the function $f(x)$ are $\{(0,5),(1,6),(2,9)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=x^{2}+5$ $\newline$ $f(x)=x+5$ $\newline$ $f(x)=5 \cdot\left(\frac{6}{5}\right)^{x}$ $\newline$ $f(x)=3 x+3$

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