The graph below shows two polynomial functions, f(x) and g(x): Which of the following statements is

10 answers
Question:

The graph below shows two polynomial functions, f(x) and g(x):
Which of the following statements is true about the graph above?
a. f(x) is an even degree polynomial with a positive leading coefficient.
b. g(x) is an even degree polynomial with a positive leading coefficient.
c. f(x) is an odd degree polynomial with a negative leading coefficient.
d. g(x) is an odd degree polynomial with a negative leading coefficient.

[tex]The graph below shows two polynomial functions, f(x) and g(x): Which of the following statements is[/tex]


Answers

f(x) has the greater maximum ⇒ 1st statement

Step-by-step explanation:

* Lets explain how to solve the problem

- The quadratic function represented graphically by a parabola with

 minimum point or maximum point

- If the parabola is opened upward then its vertex is minimum, and is

 it is opened downward then its vertex is maximum

- The form of the quadratic function is f(x) = ax² + bx + c, where

  a , b , c are constant

- The vertex of the parabola is (h , k), where h = -b/2a and k = f(h)

- The vertex of the parabola is minimum if a is positive and maximum

 if a is negative

* Lets solve the problem

∵ The graph of f(x) has the points (-2 , -3) , (-1 , 3) , (0 , 5) , (1 , 3) , (2 , -3)

∵ The vertex of the parabola has the greatest value of y when it's

  opened downward

∵ The x-coordinate of the vertex point is at half the distance between

 each two x-coordinates of the opposite points

∵ The point (0 , 5) has the greatest y-coordinate

∵ Its x-coordinate = (-1 + 1)/2 = 0 or (-2 + 2)/2 = 0

∴ The vertex of f(x) is (0 , 5)

∴ The maximum value of f(x) is 5

∵ g(x) = -x² + 4

∵ The general form of g(x) = ax² + bx + c

∴ a = -1 , b = 0 , c = 4

- Lets calculate the x-coordinate of the vertex point using the

 rule above

∵ h = -b/2a

∴ h = 0/2(-1) = 0

∵ k = g(h)

∴ k = g(0) = -(0)² + 4 = 4

∴ The vertex of g(x) = (0 , 4)

∵ a is negative , then the vertex point is maximum

∴ The maximum value of g(x) is 4

∵ The maximum value of f(x) is 5 and the maximum value of g(x) is 4

∴ f(x) has the greater maximum.

f(x) is an even degree polynomial with a positive leading coefficient.

Step-by-step explanation:

both sides of f(x) are pointed in the same direction so its an even degree and the leading coefficient is pointed up so its positive

I believe that the third, fifth, and sixth answers are correct, just took the quiz. But if you could tell me the exact problem that would be great.

Step-by-step explanation:

The correct option is 1.

Step-by-step explanation:

From the given table is notices that the function f(x) is a downward parabola.

The maximum value of f(x) is 5 at x=1.

The function g(x) is

[tex]g(x)=-x^2+4x[/tex]

vertex of the parabola is

[tex](\frac{-b}{2a}, g(\frac{-b}{2a}))[/tex]

[tex](\frac{-4}{2\times 1}, g(\frac{-4}{2\times 1})[/tex]

[tex](2, g(2))[/tex]

Put x=2.

[tex]g(x)=-2^2+4(2)=4[/tex]

Therefore the vertex of g(x) is (2,4). The vertex of a downward parabola is the maximum point of the function.

Therefore ƒ(x) has the greater maximum. Option 1 is correct.

The first statement is true.

Step-by-step explanation:

The first statement is true: f(x) is  the graph of a trinomial of even degree 2 and a positive leading coefficient.

The second statement is not true. It is a polynomial of degree 3.

The third statement is untrue ( it is of even degree).

The last statement is untrue - it has a positive leading coefficient.

A. g(x) is an even degree polynomial with a positive leading coefficient.
because g(x) curves upward at both ends

Answers: the graph is translated down 1 unit and the domain and range of g(x) is the same as the domain and range of f(x).

B and D are the correct answers. 

Hello there.

Which of the following statements is true about the graph above?

A. g(x) is an even degree polynomial with a positive leading coefficient.

It could be (a), since g(x) is symmetrical when cut downward s

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