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
all are right except for the last one - I think
YES ITS RIGHT
To determine the end behavior of a polynomial function, you need to consider the leading term, which is the term with the highest degree.
In the first polynomial, f(x) = 2x^2 - 2x - 2, the leading term is 2x^2. Since the leading coefficient (2) is positive, the polynomial rises to the left (as x approaches negative infinity) and rises to the right (as x approaches positive infinity).
In the second polynomial, f(x) = -3x^2 - 2x - 3, the leading term is -3x^2. Since the leading coefficient (-3) is negative, the polynomial falls to the left (as x approaches negative infinity) and falls to the right (as x approaches positive infinity).
In the third polynomial, f(x) = 6x^3 - 3x^2 - 3x - 2, the leading term is 6x^3. Since the leading coefficient (6) is positive, the polynomial rises to the left (as x approaches negative infinity) and rises to the right (as x approaches positive infinity).
To match the function with its graph, you would need to provide the options or descriptions of the graphs for each function.
To check your work using the Leading Coefficient Test, you need to examine the leading coefficient of each polynomial function.
The Leading Coefficient Test states that if the leading coefficient of a polynomial is positive, the end behavior of the function is that it rises to the right and rises to the left. On the other hand, if the leading coefficient is negative, the end behavior of the function is that it falls to the right and falls to the left.
Let's apply this test to the given polynomial functions:
1. f(x) = 2x^2 - 2x - 2
The leading coefficient is positive (2), so your answer is correct. The function rises to the right (positive infinity) and rises to the left (negative infinity).
2. f(x) = -3x^2 - 2x - 3
The leading coefficient is negative (-3), so your answer is correct. The function falls to the right (negative infinity) and falls to the left (negative infinity).
3. f(x) = 6x^3 - 3x^2 - 3x - 2
The leading coefficient is positive (6), so your answer is incorrect. The function should rise to the right (positive infinity) since the leading coefficient is positive.
Now, let's discuss matching the functions with their graphs based on the end behavior.
1. f(x) = 2x^2 - 2x - 2
Since it rises to the right and rises to the left, the graph will be in the shape of a "U" or a cup open upward.
2. f(x) = -3x^2 - 2x - 3
Since it falls to the right and falls to the left, the graph will be in the shape of an inverted "U" or a cup open downward.
3. f(x) = 6x^3 - 3x^2 - 3x - 2
As mentioned earlier, this function rises to the right and not falls. Therefore, it does not match the end behavior described.
Remember to always check the leading coefficient and apply the Leading Coefficient Test to determine the end behavior correctly.