Answered: Sketch this graph on a sheet of paper.…

Name: **Graph Description:**The graph shows a piecewise linear function $
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Description: **Graph Description:**The graph shows a piecewise linear function \( f(x) $ with two segments:1. The first segment (red) starts from $(-7, -3)$ and ends at $(0, 0)$.2. The second segment (green) starts from $(0, 0)$ and ends at $(3, 3)$.All

Math

Calculus

Sketch this graph on a sheet of paper. Now we want to find g(x) = - 2f(x+ 1) - 3 Be sure to list the transformations to be done. Show the transformations being done and the final product.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Topic Video

Question

**Graph Description:**

The graph shows a piecewise linear function $ f(x) $ with two segments:

1. The first segment (red) starts from $(-7, -3)$ and ends at $(0, 0)$.
2. The second segment (green) starts from $(0, 0)$ and ends at $(3, 3)$.

All segments connect through solid points at $(-7, -3)$, $(0, 0)$, and $(3, 3)$.

**Instructions:**

Consider the graph of $ f(x) $ above.

- Sketch this graph on a sheet of paper.
- Now, we want to find $ g(x) = -2f(x+1) - 3 $.
- Be sure to list the transformations to be done.

### Transformations:

1. **Horizontal Shift:** Shift the graph 1 unit to the left due to $(x + 1)$.
2. **Vertical Stretch and Reflection:** Multiply the $ y $-values by $-2$, resulting in a vertical stretch by a factor of 2 and reflection across the $ x $-axis.
3. **Vertical Shift:** Shift the graph down by 3 units.

- Show the transformations being done and the final product.

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