Answer:
The x-intercept is x = -2, and the graph approaches a vertical asymptote at x = -3.
Step-by-step explanation:
The given graph is a transformed logarithm function.
The graph is obtained by shifting the parent function three units left.
The vertical asymptote is now

The x-intercept is where the graph intersect the x-axis, which is x=-2
Therefore the last option is correct.
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.
<h3>Calculation:</h3>
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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5/3 each friend gets 3/5 of the trail mix
1) Type of motion: constant acceleration.
2) acceleration, a = 9.8 m/s^2
3) time up = time down = 4seconds / 2 = 2 seconds
4) formula = Vf = Vo - a*t^2/2
Vf = 0 => Vo = a*t^2 / 2 = 9.8m/s^2 * (2 s)^2 / 2 = 19.6 m/s
Answer: 19.6 m/s