Question

question 5 of 19 (1 point) | question attempt: 5 of unlimited
use the graph to answer the following questions.
(a) over which intervals is the function decreasing? choose all that apply.
□ (-∞, -6) □ (-6, -3) □ (-3, 1) □ (-6, 1) □ (1, ∞)

Explanation:

Step1: Recall decreasing function definition

A function is decreasing on an interval if, as \( x \) increases, \( y \) decreases (the graph falls from left to right).

Step2: Analyze each interval

• For \( (-\infty, -6) \): As \( x \) moves from \( -\infty \) to \( -6 \), the graph rises ( \( y \) increases), so not decreasing.
• For \( (-6, -3) \): As \( x \) moves from \( -6 \) to \( -3 \), the graph falls ( \( y \) decreases), so decreasing.
• For \( (-3, 1) \): As \( x \) moves from \( -3 \) to \( 1 \), the graph rises ( \( y \) increases), so not decreasing.
• For \( (-6, 1) \): This interval includes both decreasing (\( -6 \) to \( -3 \)) and increasing (\( -3 \) to \( 1 \)) parts, so not entirely decreasing.
• For \( (1, \infty) \): As \( x \) moves from \( 1 \) to \( \infty \), the graph falls ( \( y \) decreases), so decreasing.

Answer:

\( (-6, -3) \), \( (1, \infty) \) (the corresponding checkboxes for these intervals should be selected)