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Three points on the graph of the function f(x) are {(0,6),(1,7),(2,8)}. Which equation represents f(x) ? f(x)=x^(2)+6 f(x)=x+6 f(x)=6*((7)/(6))^(x) f(x)=x-6

Three points on the graph of the function f(x) f(x) are {(0,6),(1,7),(2,8)} \{(0,6),(1,7),(2,8)\} . Which equation represents f(x) f(x) ?\newlinef(x)=x2+6 f(x)=x^{2}+6 \newlinef(x)=x+6 f(x)=x+6 \newlinef(x)=6⋅(76)x f(x)=6 \cdot\left(\frac{7}{6}\right)^{x} \newlinef(x)=x−6 f(x)=x-6

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Q. Three points on the graph of the function f(x) f(x) are {(0,6),(1,7),(2,8)} \{(0,6),(1,7),(2,8)\} . Which equation represents f(x) f(x) ?\newlinef(x)=x2+6 f(x)=x^{2}+6 \newlinef(x)=x+6 f(x)=x+6 \newlinef(x)=6⋅(76)x f(x)=6 \cdot\left(\frac{7}{6}\right)^{x} \newlinef(x)=x−6 f(x)=x-6
  1. Test Function 0,60,6: Let's test each function with the given points to see which one fits all three points.\newlineFirst, we will test the point 0,60,6 in each function.
  2. Test Function 1,71,7: Test the function f(x)=x2+6f(x)=x^2+6 with the point 0,60,6.f(0)=02+6=6f(0) = 0^2 + 6 = 6. This matches the given point 0,60,6.
  3. Test Function 2,82,8: Test the function f(x)=x+6f(x)=x+6 with the point 0,60,6.f(0)=0+6=6f(0) = 0 + 6 = 6. This also matches the given point 0,60,6.
  4. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6.This also matches the given point (0,6)(0,6).Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6).f(0)=6×(7/6)0=6×1=6f(0) = 6\times(7/6)^0 = 6\times1 = 6.This matches the given point (0,6)(0,6) as well.
  5. Test Function (2,8)(2,8): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6. This also matches the given point (0,6)(0,6).Test the function f(x)=6×(76)xf(x)=6\times\left(\frac{7}{6}\right)^x with the point (0,6)(0,6).f(0)=6×(76)0=6×1=6f(0) = 6\times\left(\frac{7}{6}\right)^0 = 6\times1 = 6. This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).f(x)=x+6f(x)=x+611. This does not match the given point (0,6)(0,6). We can eliminate this function as a possible representation of f(x)=x+6f(x)=x+633.
  6. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6. This also matches the given point (0,6)(0,6).Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6).f(0)=6×(7/6)0=6×1=6f(0) = 6\times(7/6)^0 = 6\times1 = 6. This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).(0,6)(0,6)00. This does not match the given point (0,6)(0,6). We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.
  7. Test Function (2,8)(2,8): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6. This also matches the given point (0,6)(0,6).Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6).f(0)=6×(7/6)0=6×1=6f(0) = 6\times(7/6)^0 = 6\times1 = 6. This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).f(x)=x+6f(x)=x+611. This does not match the given point (0,6)(0,6). We can eliminate this function as a possible representation of f(x)=x+6f(x)=x+633.Now, let's test the point f(x)=x+6f(x)=x+644 in the remaining functions.Test the function f(x)=x+6f(x)=x+655 with the point f(x)=x+6f(x)=x+644.f(x)=x+6f(x)=x+677. This matches the given point f(x)=x+6f(x)=x+644.
  8. Test Function 2,82,8: Test the function f(x)=x+6f(x)=x+6 with the point $0,6\$0,6\). \(\newlinef(0) = 0 + 6 = 6\). This also matches the given point $0,6\$0,6\).Test the function f(x)=6∗(7/6)xf(x)=6*(7/6)^x with the point $0,6\$0,6\). \(\newlinef(0) = 6*(7/6)^0 = 6*1 = 6\). This matches the given point $0,6\$0,6\) as well.Test the function f(x)=x−6f(x)=x-6 with the point $0,6\$0,6\). f(x)=x+6f(x)=x+611. This does not match the given point $0,6\$0,6\). We can eliminate this function as a possible representation of f(x)=x+6f(x)=x+633.Now, let's test the point f(x)=x+6f(x)=x+644\) in the remaining functions.Test the function f(x)=x+6f(x)=x+655 with the point f(x)=x+6f(x)=x+644\). f(x)=x+6f(x)=x+677. This matches the given point f(x)=x+6f(x)=x+644\).Test the function f(x)=x+6f(x)=x+6 with the point f(x)=x+6f(x)=x+644\). $0,6\$0,611. This also matches the given point f(x)=x+6f(x)=x+644\).
  9. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6.This also matches the given point (0,6)(0,6).Test the function f(x)=6⋅(76)xf(x)=6\cdot\left(\frac{7}{6}\right)^x with the point (0,6)(0,6).f(0)=6⋅(76)0=6⋅1=6f(0) = 6\cdot\left(\frac{7}{6}\right)^0 = 6\cdot1 = 6.This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).(0,6)(0,6)00.This does not match the given point (0,6)(0,6).We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.Test the function (0,6)(0,6)44 with the point (0,6)(0,6)33.(0,6)(0,6)66.This matches the given point (0,6)(0,6)33.Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 600.This also matches the given point (0,6)(0,6)33.Test the function f(x)=6⋅(76)xf(x)=6\cdot\left(\frac{7}{6}\right)^x with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 644.This matches the given point (0,6)(0,6)33 as well.
  10. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6.This also matches the given point (0,6)(0,6).Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6).f(0)=6×(7/6)0=6×1=6f(0) = 6\times(7/6)^0 = 6\times1 = 6.This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).(0,6)(0,6)00.This does not match the given point (0,6)(0,6).We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.Test the function (0,6)(0,6)44 with the point (0,6)(0,6)33.(0,6)(0,6)66.This matches the given point (0,6)(0,6)33.Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 600.This also matches the given point (0,6)(0,6)33.Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 644.This matches the given point (0,6)(0,6)33 as well.Finally, let's test the point f(0)=0+6=6f(0) = 0 + 6 = 666 in the remaining functions.
  11. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6.This also matches the given point (0,6)(0,6).Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6).f(0)=6×(7/6)0=6×1=6f(0) = 6\times(7/6)^0 = 6\times1 = 6.This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).(0,6)(0,6)00.This does not match the given point (0,6)(0,6).We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.Test the function (0,6)(0,6)44 with the point (0,6)(0,6)33.(0,6)(0,6)66.This matches the given point (0,6)(0,6)33.Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 600.This also matches the given point (0,6)(0,6)33.Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 644.This matches the given point (0,6)(0,6)33 as well.Finally, let's test the point f(0)=0+6=6f(0) = 0 + 6 = 666 in the remaining functions.Test the function (0,6)(0,6)44 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.f(0)=0+6=6f(0) = 0 + 6 = 699.This does not match the given point f(0)=0+6=6f(0) = 0 + 6 = 666.We can eliminate this function as a possible representation of (0,6)(0,6)22.
  12. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6. This also matches the given point (0,6)(0,6).Test the function f(x)=6∗(7/6)xf(x)=6*(7/6)^x with the point (0,6)(0,6).f(0)=6∗(7/6)0=6∗1=6f(0) = 6*(7/6)^0 = 6*1 = 6. This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).(0,6)(0,6)00. This does not match the given point (0,6)(0,6). We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.Test the function (0,6)(0,6)44 with the point (0,6)(0,6)33.(0,6)(0,6)66. This matches the given point (0,6)(0,6)33.Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 600. This also matches the given point (0,6)(0,6)33.Test the function f(x)=6∗(7/6)xf(x)=6*(7/6)^x with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 644. This matches the given point (0,6)(0,6)33 as well.Finally, let's test the point f(0)=0+6=6f(0) = 0 + 6 = 666 in the remaining functions.Test the function (0,6)(0,6)44 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.f(0)=0+6=6f(0) = 0 + 6 = 699. This does not match the given point f(0)=0+6=6f(0) = 0 + 6 = 666. We can eliminate this function as a possible representation of (0,6)(0,6)22.Test the function f(x)=x+6f(x)=x+6 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.(0,6)(0,6)44. This matches the given point f(0)=0+6=6f(0) = 0 + 6 = 666.
  13. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).
    f(0)=0+6=6f(0) = 0 + 6 = 6.
    This also matches the given point (0,6)(0,6).Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6).
    f(0)=6×(7/6)0=6×1=6f(0) = 6\times(7/6)^0 = 6\times1 = 6.
    This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).
    (0,6)(0,6)00.
    This does not match the given point (0,6)(0,6).
    We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.Test the function (0,6)(0,6)44 with the point (0,6)(0,6)33.
    (0,6)(0,6)66.
    This matches the given point (0,6)(0,6)33.Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6)33.
    f(0)=0+6=6f(0) = 0 + 6 = 600.
    This also matches the given point (0,6)(0,6)33.Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point (0,6)(0,6)33.
    f(0)=0+6=6f(0) = 0 + 6 = 644.
    This matches the given point (0,6)(0,6)33 as well.Finally, let's test the point f(0)=0+6=6f(0) = 0 + 6 = 666 in the remaining functions.Test the function (0,6)(0,6)44 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.
    f(0)=0+6=6f(0) = 0 + 6 = 699.
    This does not match the given point f(0)=0+6=6f(0) = 0 + 6 = 666.
    We can eliminate this function as a possible representation of (0,6)(0,6)22.Test the function f(x)=x+6f(x)=x+6 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.
    (0,6)(0,6)44.
    This matches the given point f(0)=0+6=6f(0) = 0 + 6 = 666.Test the function f(x)=6×(7/6)xf(x)=6\times(7/6)^x with the point f(0)=0+6=6f(0) = 0 + 6 = 666.
    (0,6)(0,6)88.
    This does not match the given point f(0)=0+6=6f(0) = 0 + 6 = 666.
    We can eliminate this function as a possible representation of (0,6)(0,6)22.
  14. Test Function (22,88): Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6).f(0)=0+6=6f(0) = 0 + 6 = 6.This also matches the given point (0,6)(0,6).Test the function f(x)=6⋅(76)xf(x)=6\cdot\left(\frac{7}{6}\right)^x with the point (0,6)(0,6).f(0)=6⋅(76)0=6⋅1=6f(0) = 6\cdot\left(\frac{7}{6}\right)^0 = 6\cdot1 = 6.This matches the given point (0,6)(0,6) as well.Test the function f(x)=x−6f(x)=x-6 with the point (0,6)(0,6).(0,6)(0,6)00.This does not match the given point (0,6)(0,6).We can eliminate this function as a possible representation of (0,6)(0,6)22.Now, let's test the point (0,6)(0,6)33 in the remaining functions.Test the function (0,6)(0,6)44 with the point (0,6)(0,6)33.(0,6)(0,6)66.This matches the given point (0,6)(0,6)33.Test the function f(x)=x+6f(x)=x+6 with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 600.This also matches the given point (0,6)(0,6)33.Test the function f(x)=6⋅(76)xf(x)=6\cdot\left(\frac{7}{6}\right)^x with the point (0,6)(0,6)33.f(0)=0+6=6f(0) = 0 + 6 = 644.This matches the given point (0,6)(0,6)33 as well.Finally, let's test the point f(0)=0+6=6f(0) = 0 + 6 = 666 in the remaining functions.Test the function (0,6)(0,6)44 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.f(0)=0+6=6f(0) = 0 + 6 = 699.This does not match the given point f(0)=0+6=6f(0) = 0 + 6 = 666.We can eliminate this function as a possible representation of (0,6)(0,6)22.Test the function f(x)=x+6f(x)=x+6 with the point f(0)=0+6=6f(0) = 0 + 6 = 666.(0,6)(0,6)44.This matches the given point f(0)=0+6=6f(0) = 0 + 6 = 666.Test the function f(x)=6⋅(76)xf(x)=6\cdot\left(\frac{7}{6}\right)^x with the point f(0)=0+6=6f(0) = 0 + 6 = 666.(0,6)(0,6)88.This does not match the given point f(0)=0+6=6f(0) = 0 + 6 = 666.We can eliminate this function as a possible representation of (0,6)(0,6)22.We have found that the function f(x)=x+6f(x)=x+6 is the only function that matches all three given points.Therefore, f(x)=x+6f(x)=x+6 represents the function (0,6)(0,6)22.

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