The rational function shown in the graph is:

<h3>
How to determine the function?</h3>
First, we can see that we have an asymptote at x = 5, so the denominator becomes equal to zero when x = 5.
Then the rational function is something like:

We also can see that when x = 6, the function intercepts the x-axis, then we must have that:
g(6) = 0
So we can define:
g(x) = x - 6
So the rational function is:

If you want to learn more about rational functions, you can read:
brainly.com/question/1851758
-1/8 because it would be -1/16 which is closer to 0 then -1/8. We want something that will return a value where the denominator is large for a negative value.
Answer:
Slope = -4
x intercept = 3
Step-by-step explanation:
See attachment for graph
Required
a. Determine the slope
b. Find the x intercept and explain what it represents
a. The slope
To calculate the slope, we start by selecting any two corresponding values of x and y from the graph.


Next, we calculate the slope (m)




b. The x intercept
This is the point where 
From the graph.
when 
This implies that:
After 3 hours, the distance left to cover is 0miles.
In other words, she arrived home in 3 hours
Answer:
.
Step-by-step explanation:
According to the Rational Root Theorem, the potential roots of a polynomial are
where, p is a factor of constant and q is a factor of leading term.
The given polynomial is

Here, 9 is the leading term and 7 is constant.
Factors of 9 are ±1, ±3, ±9.
Factors of 7 are ±1, ±7.
Using rational root theorem, the rational or potential roots are

Therefore, the potential root of f(x) are
.
Newton's Law of Cooling:

Temperature given at a time
Time
Surrounding temperature
Initial temperature
Constant (Euler's number) ≈ 2.72
Constant
Using this information, find the value of
, to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.
First, plug in the given values in the equation and solve for
:
197°,
1.5 minutes,
70° and
210°

≈ 
Let the temperature of the water cup after
minutes be 
Now, let's plug the new time and
constant in the equation and solve for
:




![x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\](https://tex.z-dn.net/?f=x%3D70%2B%7B%5Cfrac%7B140%7D%7B%5Csqrt%5B50%5D%7Be%5E%7B13%7D%7D%7D%5C%5C)

≈ 
Temperature of water after 4 minutes is 178°
sorry if there's any misspelling or wrong step but I hope my answer is correct ':3