Which of the following is written as a rational function?
2 answers:
We have to identify the rational function among the given functions.
Rational function is a function that is the ratio of two polynomials. It is rational because one polynomial is divided by the other polynomial, like a ratio.
1. Consider the first function , since it is not a function that is the ratio of two polynomials. So, it is not a rational function.
2. Consider the second function , since it is not a function that is the ratio of two polynomials. So, it is not a rational function.
3. Consider the third function , since it is not a function that is the ratio of two polynomials. So, it is not a rational function.
4. Consider the fourth function , since it is a function that is the ratio of two polynomials (x+2) and (5x). So, it is a rational function.
So, Option D is the correct answer.
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Answer:
The options are not given, so i will answer in a general way.
First, we have the system:
y + 2*x = 3
y + 2 = 3*x
To graph this system, the easier way is writing both equations as linear equations, like:
y = -2*x + 3
y = 3*x - 2
Now we just need to graph these two lines in the same coordinate axis.
To do it, we can replace the value of x by two different values in each equation, and see the correspondent value of y for these values. Then graph the two points, and draw a line that connects them.
For example, for the first equation if we have x = 0, we have:
y = -2*0 + 3
y = 3
Then we have the point (0, 3)
and if x = 1
y = -2*1 + 3 = 1
y = 1
we have the point (1, 1)
Now we only need to graph these points, and draw a line that passes through them.
Once we did this for both lines, the graph we will get will look something like the one above.
And the point where the lines intersect is the solution of the system of equations.
Which is the point (1, 1)
