Question

Match each function equation to the graphed function with the same zeros

Answer 1

Given:

Required:

We need to find the equation for the given graph.

Step-by-step 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.

`f(x)=x^3-3x^2+x-3`

Substitute x =3 in the equation.

`f(3)=(3)^3-3(3)^2+(3)-3=0`

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.

`g(x)=x^2-5x+4`

Substitute x =1 in the function.

`g(1)=(1)^2-5(1)+4=0`

We get g(1)=0

Substitute x =4 in the function.

`g(4)=(4)^2-5(4)+4=0`

We get g(4)=0.

The answer for the second graph is

`g(x)=x^2-5x+4`

Consider the third graph.

The x-intercept of the graph is (-3,0).

The zeros of the function is x =-3

Consider the function.

`k(x)=x+3`

Substitute x =-3 in the equation.

`k(-3)=-3+3=0`

We get k(-3)=0.

The answer for the third graph is

`k(x)=x+3`

Final answer:

`f(x)=x^3-3x^2+x-3`
`g(x)=x^2-5x+4`
`k(x)=x+3`