Math Problem Statement

On what intervals is the function increasing

On what intervals is the function increasing?

Solution

From the image you uploaded, the graph shows a linear function with a negative slope, meaning the function is decreasing.

Since the line is sloping downward as it moves from left to right, the function is not increasing on any interval. Instead, it is decreasing over the entire domain, which is from (,)(-\infty, \infty).

If you need further clarification or details about this function or its intervals, feel free to ask!

Here are 5 related questions to deepen understanding:

  1. What is the slope of this linear function, and how is it calculated?
  2. How can you tell if a function is increasing or decreasing by looking at its graph?
  3. How would the graph look if the function were increasing?
  4. What is the domain and range of the function in the image?
  5. How does the y-intercept of the function affect its behavior?

Tip: A function is increasing if its slope is positive, and decreasing if its slope is negative. Always check the direction of the slope when analyzing graphs.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Slopes
Graph Analysis

Formulas

Slope Formula: (y2 - y1) / (x2 - x1)

Theorems

Increasing/Decreasing Function Theorem

Suitable Grade Level

Grades 8-10