Math Problem Statement

The graph of a function is drawn below. What is the interval in which this function is decreasing?

Solution

The graph depicts a linear function with a negative slope, meaning it is decreasing over its entire domain. For a linear function with a constant negative slope, the function decreases from x=x = -\infty to x=x = \infty.

Answer:

The interval in which the function is decreasing is: (,)(-\infty, \infty)

Would you like further details on this concept or have any questions?

Here are some related questions you might find helpful:

  1. How do we determine intervals of increase or decrease for different types of functions?
  2. What does it mean for a function to be increasing or decreasing on an interval?
  3. How can we identify the slope of a linear function from its graph?
  4. What are the characteristics of a linear function with a positive slope?
  5. How does the behavior of a function differ between linear and nonlinear functions in terms of increasing and decreasing intervals?

Tip: For a function represented by a straight line, check the slope to determine if it’s increasing or decreasing; a positive slope means it increases, and a negative slope means it decreases.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Intervals of Increase/Decrease

Formulas

Slope formula (m = (y2 - y1) / (x2 - x1))

Theorems

Properties of Linear Functions

Suitable Grade Level

Grades 8-10