Question

A) list roots and multiplicity.B) domain and range C) degree : 4 D) equation (show work by solving for a)

Answer 1

A is the answer your welcome

Answer 2

A. (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.

B. Domain : (-∞, ∞)

C. Range : (-16, ∞)

D. Degree : 4

E. f(x) = (x + 3)(x + 1)(x - 1)(x - 3)

EXPLANATION :

From the problem, we have a graph in the illustration.

A. Roots are the points in which the graph intersects the x-axis.

Multiplicity means how many times the graph intersects at the specific point.

Roots :

The graph intersects at (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.

B. Domain and Range.

Domain is the set of x-values in the graph.

Range is the set of y-values in the graph.

From the graph,

Domain :

x values are all real numbers. (-∞, ∞)

Range :

y values are from y = -16 to the positive infinity. That will be (-16, ∞)

C. Degree : 4

D. The equation of a function with a degree of 4 is given by :

`f(x)=a(x-b)(x-c)(x-d)(x-e)`

where a = coefficient

b, c, d and e are the roots of the function.

Since we already solved for the roots, that will be :

b = -3, c = -1, d = 1 and e = 3

The equation will be :

`f(x)=a(x+3)(x+1)(x-1)(x-3)`

Plug in the given point (0, 9) then solve for the value of "a"

`\begin{gathered} 9=a(0+3)(0+1)(0-1)(0-3) \\ 9=a(3)(1)(-1)(-3) \\ 9=9a \\ a=(9)/(9) \\ a=1 \end{gathered}`

The equation will be :

`f(x)=(x+3)(x+1)(x-1)(x-3)`