Use the graphs of  $f$f​  and  $g$g​  to describe the transformation from the graph of  $f$f​  to the graph of $g$g​ .

The graph of $g$g​ is a verticalhorizontal translation 12345678910 unit(s) updownleftright of the graph of $f$f​ .

To describe the transformation from the graph of $ f $ to the graph of $ g $, you need to determine how the graph of $ g $ has shifted relative to $ f $. 

A **vertical translation** involves shifting the graph up or down, while a **horizontal translation** involves shifting it left or right. Here is the typical breakdown:

- **Vertical Translation**: If $ g(x) = f(x) + k $, where $ k $ is a positive number, then the graph of $ g $ is shifted **up** by $ k $ units. If $ k $ is negative, it is shifted **down** by $ |k| $ units.
- **Horizontal Translation**: If $ g(x) = f(x - h) $, where $ h $ is a positive number, then the graph of $ g $ is shifted **right** by $ h $ units. If $ h $ is negative, it is shifted **left** by $ |h| $ units.

Without the specific functions or graphs for $ f $ and $ g $, I can't determine the exact transformation. However, based on your prompt structure, you might say:

- The graph of $ g $ is a **vertical translation** $ n $ unit(s) **up/down** of the graph of $ f $.
- Or, the graph of $ g $ is a **horizontal translation** $ n $ unit(s) **left/right** of the graph of $ f $.

To determine $ n $ and the direction, examine the shift between corresponding points of $ f $ and $ g $. For example:
- If $ f(0) = 2 $ and $ g(0) = 5 $, then $ g $ is a vertical shift **up by 3 units**.
- If $ f(2) = 0 $ and $ g(4) = 0 $, then $ g $ is a horizontal shift **right by 2 units**.

Would you like more details on identifying these shifts or an example?

Here are 5 related questions:
1. How do you find the vertical shift between two graphs?
2. How does a horizontal shift affect the domain of a function?
3. What happens to a function if you reflect it across the x-axis?
4. How do vertical and horizontal stretches/compressions differ from translations?
5. What is the effect of a negative sign inside the function argument (e.g., $ f(-x) $)?

**Tip**: When analyzing graphs, always note the changes in key points like intercepts and maxima/minima to identify transformations easily.

Use the graphs of $f$ and $g$ to describe the transformation from the graph of $f$ to the graph of $g$. The graph of $g$ is a vertical or horizontal translation of 1-10 unit(s) up/down/left/right of the graph of $f$.

Learn how to describe the transformation from the graph of a function $f$ to $g$ through vertical and horizontal shifts. This problem explores function translations using key algebraic concepts such as vertical translations (g(x) = f(x) + k) and horizontal translations (g(x) = f(x - h)). Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation