Match the given polynomial function to its graph based on end behavior. f ( x ) = − 2 x 3 + x 2 + 1 f\left(x\right)=-2x^3+x^2+1 f ( x ) = − 2 x 3 + x 2 + 1

Hey, everyone. In this problem, we want to match the given polynomial function to its graph based on attend behavior. And here I have the function f of x is equal to negative 2x cubed plus x squared plus 1. So let's first determine what's going on with our end behavior by looking at that first term in standard form. Now, my function here is already written in standard form, so I can just go ahead and get started. So my very first term in standard form is this negative two x cube. So first, looking at my leading coefficient to determine what's going on on the right side, my leading coefficient is negative 2. Now because that leading coefficient is negative, my right side is going to fall down. So then determining what's going on on our ends, we're gonna take a look at our degree here, which in this case is 3. Now, 3 is an odd number. Remember, odd, opposite. So my n's are going to have the opposite behavior. So based on that, let's take a look at these graphs. I know that my right side should be falling down. So looking at the 3 graphs that I have here, it looks like in a, the right side is going up, so it is not a. And then in b, my right side is falling, so that could be an option. And then lastly, in c, my right side is also falling here, so we're between b and c. Let's consider what's going on on the ends. Now it said that our ends have the opposite behavior, so that means that my right side was falling, so my left side should be doing the opposite thing. Now looking at c here, my right side is falling, but my left side is also falling. That is not the opposite behavior so it is not c. And taking another look at b we said our right side was falling which is great and then our left side is rising, which is the opposite behavior. So our answer here is b. That's all for this one. Thanks for watching.

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0. Fundamental Concepts of Algebra3h 29m
1. Equations and Inequalities3h 27m
2. Graphs1h 43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
5. Rational Functions1h 23m
6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles40m
8. Trigonometric Functions on Right Triangles2h 5m
9. Unit Circle1h 19m
10. Graphing Trigonometric Functions1h 19m
11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 2h 34m
13. Non-Right Triangles1h 38m
14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices3h 6m
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20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m
23. Intro to Derivatives & Area Under the Curve2h 9m

4. Polynomial Functions

Understanding Polynomial Functions

Precalculus

4. Polynomial Functions

Understanding Polynomial Functions

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Multiple Choice

Match the given polynomial function to its graph based on end behavior. $f\left(x\right)=-2x^3+x^2+1$

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Identify the degree and leading coefficient of the polynomial function f(x) = -2x^3 + x^2 + 1. The degree is 3, which is odd, and the leading coefficient is -2, which is negative.

Recall that for polynomial functions with an odd degree and a negative leading coefficient, the end behavior is such that as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches positive infinity.

Analyze the graphs provided. The graph that matches the end behavior described in step 2 will start in the upper left quadrant and end in the lower right quadrant.

Compare the end behavior of each graph with the expected end behavior of the polynomial function. The correct graph should show the function decreasing as x increases and increasing as x decreases.

Select the graph that matches the end behavior of the polynomial function f(x) = -2x^3 + x^2 + 1, which is the second image provided.

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Match the given polynomial function to its graph based on end behavior. f(x)=−2x3+x2+1f\left(x\right)=-2x^3+x^2+1f(x)=−2x3+x2+1

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Match the given polynomial function to its graph based on end behavior. $f\left(x\right)=-2x^3+x^2+1$