The figure above shows the graphs of functions f and g in the xy-plane. Get 5 free video unlocks on our app with code GOMOBILE. Gauthmath helper for Chrome. Use your browser's back button to return to your test results. Question 3 Not yet answered. Which of the following could be the equation of the function graphed below?
A positive cubic enters the graph at the bottom, down on the left, and exits the graph at the top, up on the right. Solved by verified expert. Ask a live tutor for help now. Unlimited access to all gallery answers. But If they start "up" and go "down", they're negative polynomials. 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. Clearly Graphs A and C represent odd-degree polynomials, since their two ends head off in opposite directions. One of the aspects of this is "end behavior", and it's pretty easy. Step-by-step explanation: We are given four different functions of the variable 'x' and a graph.
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. 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). 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. A Asinx + 2 =a 2sinx+4. 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. This behavior is true for all odd-degree polynomials.
In all four of the graphs above, the ends of the graphed lines entered and left the same side of the picture. If you can remember the behavior for quadratics (that is, for parabolas), then you'll know the end-behavior for every even-degree polynomial. Create an account to get free access. This function is an odd-degree polynomial, so the ends go off in opposite directions, just like every cubic I've ever graphed. All I need is the "minus" part of the leading coefficient. Try Numerade free for 7 days. We solved the question!
The only graph with both ends down is: Graph B. This problem has been solved! Graph D shows both ends passing through the top of the graphing box, just like a positive quadratic would. SAT Math Multiple Choice Question 749: Answer and Explanation.
The only equation that has this form is (B) f(x) = g(x + 2). Answer: The answer is. These traits will be true for every even-degree polynomial. 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.
High accurate tutors, shorter answering time. ← swipe to view full table →. 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. To unlock all benefits! Thus, the correct option is. Answered step-by-step. Gauth Tutor Solution.
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