we know that
If the point belongs to the graph, then the point must satisfy the equation
we will proceed to verify each case
case A.) \(f(x)=4(x^{5})\)
The point is \((2,80)\)
Verify if the point satisfy the equation
For \(x=2\) find the value of y in the equation and compare with the y-coordinate of the point
\(f(2)=4(2^{5})\)
\(f(2)=128\)
\(128
eq 80\)
therefore
the equation \(f(x)=4(x^{5})\) not passes through the point \((2,80)\)
case B.) \(f(x)=5(x^{4})\)
The point is \((2,80)\)
Verify if the point satisfy the equation
For \(x=2\) find the value of y in the equation and compare with the y-coordinate of the point
\(f(2)=5(2^{4})\)
\(f(2)=80\)
\(80=80\)
therefore
the equation \(f(x)=5(x^{4})\) passes through the point \((2,80)\)
case C.) \(f(x)=4(5^{x})\)
The point is \((2,80)\)
Verify if the point satisfy the equation
For \(x=2\) find the value of y in the equation and compare with the y-coordinate of the point
\(f(2)=4(5^{2})\)
\(f(2)=100\)
\(100
eq 80\)
therefore
the equation \(f(x)=4(5^{x})\) not passes through the point \((2,80)\)
case D.) \(f(x)=5(4^{x})\)
The point is \((2,80)\)
Verify if the point satisfy the equation
For \(x=2\) find the value of y in the equation and compare with the y-coordinate of the point
\(f(2)=5(4^{2})\)
\(f(2)=80\)
\(80=80\)
therefore
the equation \(f(x)=5(4^{x})\) passes through the point \((2,80)\)
therefore
the answer is
\(f(x)=5(x^{4})\)
\(f(x)=5(4^{x})\)
