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Which of the following could be the equation of the function graphed below? Use your browser's back button to return to your test results. If you can remember the behavior for cubics (or, technically, for straight lines with positive or negative slopes), then you will know what the ends of any odd-degree polynomial will do. Clearly Graphs A and C represent odd-degree polynomials, since their two ends head off in opposite directions. When the graphs were of functions with negative leading coefficients, the ends came in and left out the bottom of the picture, just like every negative quadratic you've ever graphed.
Answered step-by-step. By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. Now let's look at some polynomials of odd degree (cubics in the first row of pictures, and quintics in the second row): As you can see above, odd-degree polynomials have ends that head off in opposite directions. Advanced Mathematics (function transformations) HARD. When you're graphing (or looking at a graph of) polynomials, it can help to already have an idea of what basic polynomial shapes look like. High accurate tutors, shorter answering time. Therefore, the end-behavior for this polynomial will be: "Down" on the left and "up" on the right. In all four of the graphs above, the ends of the graphed lines entered and left the same side of the picture.
12 Free tickets every month. But If they start "up" and go "down", they're negative polynomials. Recall from Chapter 9, Lesson 3, that when the graph of y = g(x) is shifted to the left by k units, the equation of the new function is y = g(x + k). Enjoy live Q&A or pic answer. The figure above shows the graphs of functions f and g in the xy-plane. All I need is the "minus" part of the leading coefficient. Create an account to get free access. Y = 4sinx+ 2 y =2sinx+4. The figure clearly shows that the function y = f(x) is similar in shape to the function y = g(x), but is shifted to the left by some positive distance. Thus, the correct option is. ← swipe to view full table →. Question 3 Not yet answered. Step-by-step explanation: We are given four different functions of the variable 'x' and a graph. Since the leading coefficient of this odd-degree polynomial is positive, then its end-behavior is going to mimic that of a positive cubic.
Matches exactly with the graph given in the question. The only equation that has this form is (B) f(x) = g(x + 2). Always best price for tickets purchase. The attached figure will show the graph for this function, which is exactly same as given. To check, we start plotting the functions one by one on a graph paper. Graph D shows both ends passing through the top of the graphing box, just like a positive quadratic would.
The actual value of the negative coefficient, −3 in this case, is actually irrelevant for this problem. Check the full answer on App Gauthmath. The only graph with both ends down is: Graph B. This behavior is true for all odd-degree polynomials. We solved the question!
SAT Math Multiple Choice Question 749: Answer and Explanation. We'll look at some graphs, to find similarities and differences. If you can remember the behavior for quadratics (that is, for parabolas), then you'll know the end-behavior for every even-degree polynomial. Provide step-by-step explanations. To answer this question, the important things for me to consider are the sign and the degree of the leading term. Since the sign on the leading coefficient is negative, the graph will be down on both ends. The exponent says that this is a degree-4 polynomial; 4 is even, so the graph will behave roughly like a quadratic; namely, its graph will either be up on both ends or else be down on both ends. A positive cubic enters the graph at the bottom, down on the left, and exits the graph at the top, up on the right.
One of the aspects of this is "end behavior", and it's pretty easy. These traits will be true for every even-degree polynomial. If they start "down" (entering the graphing "box" through the "bottom") and go "up" (leaving the graphing "box" through the "top"), they're positive polynomials, just like every positive cubic you've ever graphed. Ask a live tutor for help now. SAT Math Multiple-Choice Test 25.
Unlimited answer cards. Gauthmath helper for Chrome. First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients: Content Continues Below. Get 5 free video unlocks on our app with code GOMOBILE. Answer: The answer is.
This problem has been solved! This polynomial is much too large for me to view in the standard screen on my graphing calculator, so either I can waste a lot of time fiddling with WINDOW options, or I can quickly use my knowledge of end behavior. Solved by verified expert.