The table gives values for a polynomial function 𝑔 at selected values of 𝑥. If 𝑎<𝑏, then 𝑔𝑎>𝑔𝑏 for all 𝑎 and 𝑏 in the interval 3<𝑥<7. Which of the following could be true about the graph of 𝑔 on the interval 3<𝑥<7 ?ResponsesThe graph of 𝑔 is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of  g  is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of 𝑔 is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of  g  is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of 𝑔 is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.The graph of  g  is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.The graph of 𝑔 is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.

QuestionThe graph of the function g is shown above. If f is the function given by 𝑓(𝑥) =𝑔(𝑔(𝑥)) , what is the value of  𝑓'(0) ?Responses−2negative 2−1negative 1223

The first derivative of the function f is defined by f'(x) = (x2 +1)sin(3x - 1) for -1.5 < x < 1.5. On which of the following intervals is the graph of f concave up?Responses(−1.5, −1.341) and (−0.240, 0.964)(−1.5, −1.341) and (−0.240, 0.964)(−1.341, −0.240) and (0.964, 1.5)(−1.341, −0.240) and (0.964, 1.5)(−0.714, 0.333) and (1.381, 1.5)(−0.714, 0.333) and (1.381, 1.5)(−1.5, −0.714) and (0.333, 1.381)

Which facts are true for the graph of the function below? Check all that apply.𝐹(𝑥)=(35)𝑥F(x)=( 53​ ) x A.It is increasing.B.The domain of F(x) is x > 0.C.It is decreasing.D.The range of F(x) is y > 0.E.The x-intercept is (1, 0).F.The y-intercept is (0, 1).SUBMITarrow_backPREVIOUS

he graph of a function f is given. Use the graph to estimate the following.(a) All the local maximum and minimum values of the function and the value of x at which each occurslocal maximum     (x, y) = 0,12 local minimum      (x, y) = −9,−6 (smaller x-value)local minimum (x, y) = 6,3 (larger x-value)(b) The intervals on which the function is increasing and on which the function is decreasing. (Enter your answers using interval notation.)increasing     (−∞,−9)∪(0,6) decreasing     (0,6)

Partially Correct(d): Answer all the questions before selecting Check.Try one last timeBelow is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.y246810-2-4-6-8-10x2468-2-4-6-8-10Use the graph to answer the following questions.(a) Over which intervals is the function decreasing? Choose all that apply.−−∞, 8−−8, 1−1, 5−8, 55, ∞(b) At which x-values does the function have local maxima? If there is more than one value, separate them with commas.1(c) What is the sign of the function's leading coefficient? (d) Which of the following is a possibility for the degree of the function? Choose all that apply.456789