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Free_Kalibri [48]
3 years ago
10

Solve. High school pre-cal

Mathematics
1 answer:
Oliga [24]3 years ago
8 0

Answer:

<em>Answer: Quadrant 4</em>

Step-by-step explanation:

<u>Graph of Functions </u>

Let's analyze the function  

\displaystyle y=\frac{x^2+3x}{x+1}

To better understand the following analysis, we'll factor y

\displaystyle y=\frac{x(x+3)}{x+1}

For y to have points in the first quadrant, at least one positive value of x must produce one positive value of y. It's evident that any x greater than 0 will do. For example, x=1 will make y to be positive in the numerator and in the denominator, so it's positive

For y to have points in the second quadrant, at least one negative value of x must produce one positive value of y. We need two of the factors that are negative. It can be seen that x=-2 will make y as positive, going through the second quadrant.

For the third quadrant, we have to find at least one value of x who produces a negative value of y. We only need to pick a value of x that makes one or all the factors be negative. For example, x=-4 produces a negative value of y, so it goes through the third quadrant

Finally, the fourth quadrant is never reached by any branch because no positive value of x can produce a negative value of y.

Answer: Quadrant 4

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