Answer:
y=1 for ![y\leq 1](https://tex.z-dn.net/?f=y%5Cleq%201)
Step-by-step explanation:
We can solve an inequality much like we solve an equation. We will use inverse operations to isolate y. If we need to divide by a negative then we will need to flip the inequality.
![2y+9\leq 11\\2y+9-9\leq 11-9\\2y\leq 2\\\frac{2y}{2}\leq \frac{2}{2} \\y\leq 1](https://tex.z-dn.net/?f=2y%2B9%5Cleq%2011%5C%5C2y%2B9-9%5Cleq%2011-9%5C%5C2y%5Cleq%202%5C%5C%5Cfrac%7B2y%7D%7B2%7D%5Cleq%20%20%5Cfrac%7B2%7D%7B2%7D%20%5C%5Cy%5Cleq%201)
First, we moved 9 across the equal sign to combine it with 11 by subtracting by 9 from both sides.
Second, we divided both sides by 2.
is the solution. All solutions equal to 1 and less than 1 will work.
3(3^8) this is how you write it as power. however if you simplify it will be 19683 ft
The equation for a rational function with: Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is
![y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}](https://tex.z-dn.net/?f=y%3D-36%5Cfrac%7B%28x%20-%201%29%20%28x%20-%204%29%7D%7B%28x%20-%202%29%20%28x%20%2B4%29%7D)
<h3>How to determine the equation for a
rational function</h3>
<u>information gotten from the question</u>
From the question given above, the following data were obtained:
- Vertical asymptotes at x = 2 and x = -4
- x-intercepts at x = 1 and x = 4
- y-intercept at 9
- y =?
Rational function means that the equation will be a fraction
The rational function that models the Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is written as follows
The numerator
x-intercepts at x = 1 and x = 4
x = 1 ⇒ (x - 1)
x = 4 ⇒ (x - 4)
This means the equation will have (x - 1) (x - 4) as the numerator
The denominator
Vertical asymptotes at x = 2 and x = -4
x = 2 ⇒ (x - 2)
x = -4 ⇒ (x + 4)
This means the equation will have (x - 2) (x + 4) as the denominator
y-intercept at 9
expressing the functions derived already gives
![y=a\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}](https://tex.z-dn.net/?f=y%3Da%5Cfrac%7B%28x%20-%201%29%20%28x%20-%204%29%7D%7B%28x%20-%202%29%20%28x%20%2B4%29%7D)
substituting x = 0 and y = 9 and solving gives a
![9=a\frac{(0 - 1) (0 - 4)}{(0 - 2) (0 +4)}](https://tex.z-dn.net/?f=9%3Da%5Cfrac%7B%280%20-%201%29%20%280%20-%204%29%7D%7B%280%20-%202%29%20%280%20%2B4%29%7D)
![9=a\frac{(4)}{(-8)}](https://tex.z-dn.net/?f=9%3Da%5Cfrac%7B%284%29%7D%7B%28-8%29%7D)
4a = 9 * -8
a = -36
The equation of the rational function is ![y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}](https://tex.z-dn.net/?f=y%3D-36%5Cfrac%7B%28x%20-%201%29%20%28x%20-%204%29%7D%7B%28x%20-%202%29%20%28x%20%2B4%29%7D)
Learn more on equation for a rational function at :
brainly.com/question/28032338
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Thhe graph of a linear relationship will be a straight line.
Non linear would be a curve.