file:///C:/Users/Pat/Downloads/IMG_0166.JPG
Above is a graph of a polynomial function ƒ with real coefficients. Use graph to answer following questions about ƒ. All local extreme of ƒ are shown on graph.
a. the function is decreasing over which intervals? Choose all that apply. 1. (-∞,-5) 2. (-5,-3)
3. (-5,0) 4. (0,3) 5. (6,8) 6.(8,∞)
b. The function f has local maxima at which x-values? If there is more than one value, separate with comas.
c. What is the sign of the leading coefficient of? 1. positive 2. negative or 3. not enough info
d. Which of the following is a possibility for the degree of f? Choose all that apply. a.4 b.5 c.6 d.7 e.8 f.9
I have answered questions a, b, & c correctly just can't get question d right I thought is was 5, 7, 9 but was told that is wrong. Please help
sorry - files on your C: drive are not available to us.
To answer question d, we need to determine the degree of the polynomial function ƒ based on the given graph.
The degree of a polynomial function is the highest power of the variable in the function. We can find the degree by looking at the number of turning points on the graph.
In this case, the graph appears to have three turning points: a local minimum at x = -3, a local maximum at x = 0, and another local maximum at x = 6.
Since we have three turning points, the degree of the polynomial function is typically expected to be one less than the number of turning points. However, we also need to consider the behavior of the graph as it approaches infinity on both ends.
Looking at the graph, as x approaches negative infinity, the function appears to be decreasing. As x approaches positive infinity, the function seems to be increasing.
For a polynomial function with an even degree, if the graph is decreasing as x approaches negative infinity and increasing as x approaches positive infinity, then the leading coefficient must be positive. Conversely, if the graph is increasing as x approaches negative infinity and decreasing as x approaches positive infinity, then the leading coefficient must be negative.
Based on the given graph and the behavior of the function as x approaches negative and positive infinity, we can conclude that the leading coefficient is positive. Therefore, the correct answer for question c is 1. positive.
Now let's determine the degree of the polynomial function. Since we have a positive leading coefficient and an odd number of turning points, it is safe to say that the degree of the function is an odd number.
Given the options provided for question d (a. 4, b. 5, c. 6, d. 7, e. 8, f. 9), we can eliminate all the even numbers (a. 4, c. 6, e. 8) because the degree must be odd in this case.
Therefore, the correct answer for question d is b. 5 and d. 7. The degree can be either 5 or 7.
I hope this helps! Let me know if you have any further questions.