Math Problem Statement
Solution
The question shown in the image asks you to analyze the graph of a function to determine where the function is increasing, decreasing, or constant. Let's go through it step by step:
-
Identifying intervals of increase: The graph shows a function that starts by decreasing and then increases. We need to identify the part where the function is increasing. From the graph, the increase occurs after , where the slope is positive.
Therefore, the function is increasing on the interval , which corresponds to option C.
-
Identifying constant intervals: A function is constant when the graph is a horizontal line, meaning the function doesn't change its value. In this graph, the function is constant between and , which is a flat part of the graph.
Thus, the function is constant on the interval , which corresponds to option D.
Would you like more detailed steps or have any questions about the graph?
Here are 5 related questions to expand on this concept:
- What is the relationship between the derivative of a function and increasing/decreasing behavior?
- Can a function have more than one interval where it is constant?
- What does it mean for a function to be decreasing, and how can we identify that on a graph?
- How can you determine the maximum or minimum points from a graph of a function?
- What role do endpoints of intervals play when discussing increasing and decreasing intervals?
Tip: When analyzing a graph, always look for changes in slope to determine increasing or decreasing behavior.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Graph Analysis
Functions
Intervals of Increase/Decrease
Constant Function
Formulas
-
Theorems
-
Suitable Grade Level
Grades 9-12
Related Recommendation
Analyzing Increasing and Decreasing Intervals of a Function from a Graph
Determine Increasing, Decreasing, and Constant Intervals on a Function Graph
Identifying Increasing, Decreasing, and Constant Intervals on a Graph
Analyzing Function Behavior: Increasing, Decreasing, and Constant Intervals
Analyze Function Behavior: Increasing, Decreasing, and Constant Intervals