Math Problem Statement
The graph of y = g(x) is shown. Draw the graph of y = 2g(x) + 4.
Solution
The problem asks you to draw the graph of based on the given graph of .
To help you adjust the graph correctly, here’s how to modify :
-
Vertical Stretch by a Factor of 2:
- Since the equation includes , the graph of will be stretched vertically by a factor of 2. This means that all points on the graph will be twice as far from the x-axis. For example, if , then ; if , then .
-
Vertical Shift by 4 Units Up:
- The "+4" in the equation shifts the graph 4 units upward. So, after applying the vertical stretch, you'll move all points up by 4 units.
Steps to draw :
- First, take each point on the graph of and multiply the y-coordinate by 2.
- Then, shift each resulting point up by 4 units on the y-axis.
Would you like more details or have any questions? Here are five related questions that might help you:
- How does a vertical stretch change the graph's appearance compared to a vertical compression?
- What would happen if the function had a negative sign in front of , like ?
- How does shifting a graph horizontally differ from shifting it vertically?
- Can you explain how to combine multiple transformations like scaling and shifting on a graph?
- What happens if both the x- and y-coordinates are transformed simultaneously?
Tip: Always apply stretching or shrinking transformations before shifting when working with function graphs.
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Math Problem Analysis
Mathematical Concepts
Function Transformations
Graphing
Vertical Stretch
Vertical Shift
Formulas
y = 2g(x) + 4
Theorems
Vertical Stretch
Vertical Shift
Suitable Grade Level
Grades 9-11