Math Problem Statement
Solution
Let's solve the problem step by step based on the given image.
(a) Rate of change for each function
Rate of change for Function 1 (Table)
The rate of change between two points and is calculated by:
Let's pick two points from the table.
For example, using points and :
So, the rate of change for Function 1 is:
Rate of change for Function 2 (Graph)
Choose two points from the graph. From the image, it looks like the points and are clear.
So, the rate of change for Function 2 is:
(b) Which function has the greater rate of change?
Since we are comparing the absolute values of the rates of change:
- Function 1:
- Function 2:
Function 2 has the greater rate of change.
Final Answer
-
(a)
- Function 1:
- Function 2:
-
(b)
Function 2 has the greater rate of change.
Do you need any further details or explanations?
Related Questions:
- How do you determine the slope from a graph?
- Why is the slope the same between any two points on a line?
- Can the rate of change be positive? What does it represent?
- How do different slopes affect the steepness of a line?
- How would the rates of change change if the graph shifted vertically?
Tip:
Always compare the absolute values of rates of change to determine which function grows or declines faster.
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Math Problem Analysis
Mathematical Concepts
Rate of Change
Linear Functions
Algebra
Formulas
Rate of Change = (y2 - y1) / (x2 - x1)
Theorems
Slope of a Line
Suitable Grade Level
Grades 8-10