A) Find the equation of the function shown in the graph: B) State the domain, Range, and End behavior for the function:

9514 1404 393

Step-by-step explanation:

The graph appears to show zeros at x=-3, x=1 and x=2. The zero at x=1 has multiplicity 2, so the factored form of the function's equation is ...

  y = (x +3)(x -1)^2(x -2)

When expanded, the equation becomes ...

  y = x^4 -x^3 -7x^2 +13x -6

This polynomial has a domain of all real numbers.

The degree is even, and the leading coefficient is positive, so this function will have a minimum value. The graph shows it as about -36. Evaluating the function in that neighborhood, we find the minimum to be an irrational number with a value of approximately -36.100456736.

The range is from about -36.1 to infinity.

Since the degree is even the end behavior will be the same for both positive and negative values of x. Since the leading coefficient is positive, the function value will tend toward positive infinity for either positive or negative large values of x.

  |x| → ∞, y → ∞

_____

Additional comment

The derivative is a cubic whose root is (-1-√209)/8 at the minimum of the function. This means the function's minimum value is (-9419 -627√209)/512 ≈ -36.100456736016019747. The range can only be stated in symbolic form (using a radical, infinity symbol), since the actual numerical values of the limits can never be stated exactly.

y = x^4 -x^3 -7x^2 +13x -6

domain: all real numbers; range: -36.1 ≤

y < infinity

• y +∞o for Ixl → co

Step-by-step explanation:

The graph appears to show zeros at x=-3, x=1 and x=2. The zero at x=1 has multiplicity 2, so the factored form of the function's equation is...

y = (x+3)(x-1)^2(x-2)

When expanded, the equation becomes ...

y=x^4 -x^3-7x^2 +13x -6

This polynomial has a domain of all real numbers.

The degree is even, and the leading coefficient is positive, so this function will have a minimum value. The graph shows it as about -36. Evaluating the function in that neighborhood, we find the minimum to be an irrational number with a value of approximately -36.100456736.

The range is from about -36.1 to infinity.

Since the degree is even the end behavior

will be the same for both positive and negative values of x. Since the leading coefficient is positive, the function value will tend toward positive infinity for either positive or negative large values of x.

Ixl → ∞, y → ∞

Additional comment

The derivative is a cubic whose root is (-1-√209)/8 at the minimum of the function. This means the function's minimum value is (-9419 -627√209)/512= -36.100456736016019747. The range can only be stated in symbolic form (using a radical, infinity symbol), since the actual numerical values of the limits can never be stated exactly.

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12

(8+64)^2= 5184 < answer

step-by-step explanation:

2^3 = 8

4^3= 64

(8+64)^2 = 5184