Math Problem Statement
Solution
From the image provided, let's analyze the graph of the function and answer the questions.
Observations:
- The graph is a straight line, indicating a linear function.
- The line crosses the -axis (x-intercept) and the -axis (y-intercept).
Answers:
-
Domain: For linear functions, the domain is all real numbers.
-
Range: Similarly, for linear functions, the range is also all real numbers.
-
Coordinates of the x-intercept: The x-intercept is where the line crosses the x-axis (). From the graph, the x-intercept is approximately at . Hence:
-
Coordinates of the y-intercept: The y-intercept is where the line crosses the y-axis (). From the graph, the y-intercept is approximately at . Hence:
-
The function:
- From the graph, the slope () of the line can be calculated. Between and , the line decreases by 2 units vertically and increases by 4 units horizontally:
- The y-intercept () is 2. Using the slope-intercept form :
Summary of Answers:
- Domain:
- Range:
- Coordinates of the x-intercept:
- Coordinates of the y-intercept:
- The function is:
Would you like a more detailed explanation on any of these points? Here are 5 additional questions for further exploration:
- How can you verify the slope using two points on the line?
- Why is the domain of a linear function always all real numbers?
- How would the function change if the slope were positive?
- Can we determine other points on the line using the equation?
- What does the y-intercept represent in real-world applications?
Tip: When working with a graph, always identify key points like intercepts and slopes to easily deduce the function's equation.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Functions
Graph Interpretation
Formulas
Slope-Intercept Form: y = mx + b
Theorems
Properties of Linear Functions
Suitable Grade Level
Grades 8-10
Related Recommendation
Determining Domain, Range, and Intercepts from a Graph
Identify the Linear Function from a Graph - Slope and Y-Intercept
Linear Function Analysis: Identify Slope, Intercepts, and Zeros
Analyzing Linear Function Graphs: Intercepts, Domain, and Range
Find the Equation of a Line from a Graph - Linear Equations