Question

Solve. High school pre-cal

Answer 1

Answer: Quadrant 4

Explanation:

Graph of Functions

Let's analyze the function

`\displaystyle y=(x^2+3x)/(x+1)`

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

`\displaystyle y=(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