if the parent function is y=3^x describe the transformation: y=2(3)^x +7

To describe the transformation from the parent function \( y = 3^x \) to the function \( y = 2(3^x) + 7 \), we can break it down into two main transformations:

1. **Vertical Stretch**: The factor of 2 in front of \( 3^x \) indicates a vertical stretch. This means that the output values of the function are multiplied by 2. As a result, the graph will be stretched away from the x-axis.

2. **Vertical Shift**: The +7 at the end indicates a vertical shift. This means the entire graph is moved upward by 7 units. 

Putting it all together, the transformation of the parent function \( y = 3^x \) results in a graph that is vertically stretched by a factor of 2 and shifted upward by 7 units.

### Summary of Transformations:
- Vertical stretch by a factor of 2
- Vertical shift upward by 7 units

Would you like more details on any specific part of the transformation? Here are some related questions you might consider:

1. How does the vertical stretch affect specific points on the graph?
2. What would the graph look like without the vertical shift?
3. How would the transformation change if there was a horizontal shift?
4. What is the new horizontal asymptote after the transformations?
5. Can you provide examples of similar transformations with different base functions?

**Tip**: When analyzing transformations, it's helpful to sketch the original and transformed graphs for visual comparison.

Explore the transformation of the exponential function y=3^x into y=2(3^x)+7, including a vertical stretch and vertical shift. This lesson is designed for students in Grades 9-11 and covers essential concepts in transformations of functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation