Please check my work. thanxs!

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.

f(x) = 2x^2 - 2x - 2
-I got that is rises to the left and rises to the right.

f(x) = -3x^2 - 2x - 3
I got that it falls to the left and falls to the right

f(x) = 6x^3 - 3x^2 - 3x - 2
I got that it falls to the left and rises to the right

correct

To determine the end behavior of a polynomial function, you can use the Leading Coefficient Test. Here's how it works:

1. Look at the leading coefficient of the polynomial function. The leading coefficient is the coefficient of the term with the highest degree.

Now, let's apply the Leading Coefficient Test to each of the given polynomial functions:

1. f(x) = 2x^2 - 2x - 2
The leading coefficient is 2. Since the leading coefficient is positive, the polynomial will rise to the right (as x approaches positive infinity) and rise to the left (as x approaches negative infinity).

2. f(x) = -3x^2 - 2x - 3
The leading coefficient is -3. Since the leading coefficient is negative, the polynomial will fall to the right (as x approaches positive infinity) and fall to the left (as x approaches negative infinity).

3. f(x) = 6x^3 - 3x^2 - 3x - 2
The leading coefficient is 6. Since the leading coefficient is positive, the polynomial will rise to the right (as x approaches positive infinity) and fall to the left (as x approaches negative infinity).

Now, let's match the end behavior with the given function:

1. f(x) = 2x^2 - 2x - 2
Since it rises to the left and rises to the right, the graph of this function will start in the bottom left quadrant, pass through the origin, and go up towards the top right quadrant.

2. f(x) = -3x^2 - 2x - 3
Since it falls to the left and falls to the right, the graph of this function will start in the top right quadrant, pass through the origin, and go down towards the bottom left quadrant.

3. f(x) = 6x^3 - 3x^2 - 3x - 2
Since it falls to the left and rises to the right, the graph of this function will start in the top left quadrant, pass through the origin, and then rise towards the top right quadrant.

I hope this helps you check your work! Let me know if you have any more questions.