What is the graph of the function f(x) = the quantity of x plus 7, all over x minus 4?
2 answers:
Let’s sketch the graph of f(x) =
First, since this is a rational function we are going to have to be careful with division by zero issues. So, we can see from this equation that we’ll have to avoid since that will give division by zero.
Now, let’s just plug in some values of x and see what we get. Make x-y table first
x y
-20 0.542
-10 0.214
-7 0 (x intercept )
0 -1.75 (y-intercept)
3 -10
5 12
10 2.833
20 1.688
Now find the horizontal and vertical asymptotes
Vertical asymptote: Find the vertical asymptotes by setting the denominator equal to zero and solving.
Put denominator = 0
x-4 = 0
x=4
Horizontal Asymptote:
y = leading coefficient of x (in numberator )/leading coefficient of x (in denominator)
y = 1
Here is a sketch of this graph.
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Answer:
There are many.
Step-by-step explanation:
When you say proportional, you are looking for a ratio that is equivalent to the ratio given. In your case, there are many so you might need to be more specific. But still, we can help you figure it out.
An easy way to do this would be to scale it down to its simplest form and then move upwards. To find proportional ratios, just multiply denominator and the denominator with the same factor.
That is your ratio in its simplest form. Now we can scale up, I'll show you how to do one completely:
That's the same ratio scaled up by a factor of 2.
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That's the ratio given
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Scaled up by a factor of 4
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Scaled up by a factor of 5.
The list goes on and on.