Jose graphed the function f(x) = x and transformed it to create g(x) such that g(x) = 3f(x).

Which graph represents f and g?
A.
B.
C.
D.

In this case, we are working with the transformation of the function \( f(x) = x \) to \( g(x) = 3f(x) \), which becomes \( g(x) = 3x \).

### Understanding the transformations:
- \( f(x) = x \) is the equation of a straight line with a slope of 1, passing through the origin (0, 0).
- \( g(x) = 3x \) is also a straight line passing through the origin, but with a slope of 3, meaning it is steeper than \( f(x) \).

### Key points to look for in the graphs:
1. **Graph of \( f(x) = x \)**:
   - A diagonal line with slope 1, passing through points like (0, 0), (1, 1), and (-1, -1).
   
2. **Graph of \( g(x) = 3x \)**:
   - A steeper diagonal line with slope 3, passing through points like (0, 0), (1, 3), and (-1, -3).

Now, let’s examine the possible graphs based on these details:
- **Graph A**: Compare the lines, checking which one is steeper (if any).
- **Graph B**: Check if there is a clear difference between the slope of \( f(x) \) and \( g(x) \).
- **Graph C**: Look for a graph where one line has a slope of 1, and the other has a slope of 3.
- **Graph D**: Check for similar features.

Once you've checked these details, choose the graph where:
- One line has a slope of 1 (for \( f(x) \)).
- The other line has a slope of 3 (for \( g(x) \)).

If you provide the graphs, I can help you identify which one correctly represents the transformation!

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Do you want more detailed information on identifying graph transformations?

Here are 5 related questions to deepen your understanding:
1. What happens when you multiply a function by a constant factor?
2. How does the slope of a line change with different transformations?
3. What are vertical stretches in function transformations?
4. How would a graph of \( g(x) = -3x \) differ from \( f(x) = x \)?
5. What does shifting a graph horizontally or vertically look like?

**Tip:** A larger coefficient in front of \( x \) makes the graph steeper, while a smaller coefficient flattens it.

Jose graphed the function f(x) = x and transformed it to create g(x) such that g(x) = 3f(x). Which graph represents f and g? A. B. C. D.

Learn how to graph and compare the linear functions f(x) = x and its transformation g(x) = 3x. This example demonstrates function transformations, including vertical stretches and changes in slope. Suitable for students in Grades 6-8.

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