Questions: Use the graph to answer the following questions.
(a) Over which intervals is the function increasing? Choose all that apply.
(-∞,-7) (-5,-2) (-7,-2) (3,6) (6,8) (8, ∞)
(b) At which x-values does the function have local minima? If there is more than one value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
(Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all that apply.
Transcript text: se the graph to answer the following questions.
(a) Over which intervals is the function increasing? Choose all that apply.
$(-\infty,-7)$ $\qquad$ $(-5,-2)$ $\qquad$ $(-7,-2)$ $\square$ $(3,6)$ $(6,8)$ $(8, \infty)$
(b) At which $x$-values does the function have local minima? If there is more than one value, separate them with commas.
$\square$
(c) What is the sign of the function's leading coefficient?
(Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all that apply.
Solution
Solution Steps
Step 1: Find the increasing intervals
The function is increasing when the graph goes up from left to right. This happens on the intervals (-∞, -7), (-5, -2), and (8, ∞).
Step 2: Find the local minima
Local minima are the lowest points in a small neighborhood on the graph. These occur at x = 3 and x = 7.
Step 3: Determine the sign of the leading coefficient
Since the graph rises to the right and falls to the left, the leading coefficient is positive.