What translation is shown below?
2 answers:
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Answer:
Range is : { -10, -7, -5, -2 }
Step-by-step explanation:
Given:
The function is given as:
The domain of the function = { -3, 0, 2, 5 }
A function's input is called its domain and a function's output is called its range.
The range depends on the domain values. So, the values of 'y' are the values of range and the values of 'x' are the values of domain.
Here, the domain is given as:
Domain = { -3, 0, 2, 5 }
We need to find the values of 'y' for each value of 'x' taken from the domain set.
Plug in . This gives,
Plug in . This gives,
Plug in . This gives,
Plug in . This gives,
Therefore, the set of all values of 'y' is the range.
Range is equal to { -10, -7, -5, -2 }.
The simplified rational expression is (y - 3)/(y + 3). Where y ≠ -3.
<h3>How to simplify a rational expression?</h3>A rational expression is in the p/q form. Where p and q are polynomial functions.
To simplify this rational equation,
- Factorize the polynomials in both numerator and denomiantor.
- Cancel out common factors if any.
- If the denominator and the numerator have no common factors except 1, then that is said to be the simplest form of the given rational expression.
The given rational equation is
Factorizing the expression in the numerator:
y² - 12y + 27 = y² - 9y - 3y + 27
⇒ y(y - 9) - 3(y - 9)
⇒ (y - 3)(y - 9)
Factorizing the expression in the denominator:
y² - 6y - 27 = y² - 9y + 3y - 27
⇒ y(y - 9) + 3(y - 9)
⇒ (y + 3)(y - 9)
Since they have (y - 9) as the common factor, we can simplify,
⇒ (y - 3)/(y + 3) where y ≠ -3(denomiantor)
Here there are no more common factors except 1; this is the simplest form of the given rational expression.
Learn more about simplifying rational expressions here:
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