Given:
Required:
We need to find the equation for the given graph.
Explanation:
Recall that zeros of the function are the x-intercept of the graph.
Consider the first graph.
The x-intercept of the graph is (3,0).
The zero of the function satisfies the equation of the function.
Consider the function.
[tex]f(x)=x^3-3x^2+x-3[/tex]
Substitute x =3 in the equation.
[tex]f(3)=(3)^3-3(3)^2+(3)-3=0[/tex]
We get f(3)=0.
The answer for the first graph is f(x).
Consider the second graph.
The x-intercept of the graph are (1,0) and (4,0).
The zeros of the function are 1 and 4.
Consider the function.
[tex]g(x)=x^2-5x+4[/tex]
Substitute x =1 in the function.
[tex]g(1)=(1)^2-5(1)+4=0[/tex]
We get g(1)=0
Substitute x =4 in the function.
[tex]g(4)=(4)^2-5(4)+4=0[/tex]
We get g(4)=0.
The answer for the second graph is
[tex]g(x)=x^2-5x+4[/tex]
Consider the third graph.
The x-intercept of the graph is (-3,0).
The zeros of the function is x =-3
Consider the function.
[tex]k(x)=x+3[/tex]
Substitute x =-3 in the equation.
[tex]k(-3)=-3+3=0[/tex]
We get k(-3)=0.
The answer for the third graph is
[tex]k(x)=x+3[/tex]
Final answer:
[tex]f(x)=x^3-3x^2+x-3[/tex][tex]g(x)=x^2-5x+4[/tex][tex]k(x)=x+3[/tex]
