Final answer:
The equivalent form that displays values not included in the domain as constants or coefficients for the given rational function is the Piecewise form.
The answer is option ⇒D
Step-by-step explanation:
The given rational function is f(x) = (2x - 4)/(2x² + 2x - 4). The question asks for an equivalent form that displays values not included in the domain as constants or coefficients.
To find the answer, let's first determine the domain of the given function. In a rational function, the denominator cannot equal zero because it would result in division by zero, which is undefined.
Setting the denominator equal to zero, we can solve the quadratic equation 2x² + 2x - 4 = 0.
Using factoring, completing the square, or the quadratic formula, we find that the solutions are x = 1 and x = -2.
Therefore, the domain of the function excludes these values, x = 1 and x = -2.
Now, let's analyze the answer choices:
- A) Factored form: This form represents the function as a product of linear factors. It may be useful for understanding the roots of the function but does not explicitly display values not included in the domain as constants or coefficients.
- B) Standard form: This form represents the function as a ratio of polynomials, which is already the given form. It does not explicitly display values not included in the domain as constants or coefficients.
- C) Vertex form: This form is specific to quadratic functions and represents the function as a transformation of the standard form. It is not applicable to the given rational function.
- D) Piecewise form: This form represents the function as different equations for different intervals or domains. It allows explicitly displaying values not included in the domain as constants or coefficients. Therefore, the correct answer is D) Piecewise form.
In summary, the equivalent form that displays values not included in the domain as constants or coefficients for the given rational function is the Piecewise form.
The answer is option ⇒D.Piecewise form.
Your question is incomplete, but most probably the full question was:
f(x) = 2x-4/2x² + 2x - 4
A rational function is defined above. Which of the following is an equivalent form that displays values not included in the domain as constants or coefficients?
A) Factored form
B) Standard form
C) Vertex form
D) Piecewise form