The graph provided shows a transformation of $f(x) = |x|$, which is the basic absolute value function.

Observing the Graph:

1. The graph retains the V-shape of the absolute value function.
2. The slope of the graph is steeper than the standard $f(x) = |x|$.
   • In the standard function, the slope is 1 for $x > 0$ and -1 for $x < 0$.
3. Here, the slope is 2, which means the graph has been vertically stretched by a factor of 2.

Function Rule for $g(x)$:

The transformation can be written as:

$g(x) = 2|x|$

This indicates a vertical stretch of the original absolute value graph by a factor of 2.

Key Points:

• Standard Function: $f(x) = |x|$
• Transformed Function: $g(x) = 2|x|$
• The stretch factor (2) makes the graph steeper.

Let me know if you'd like further explanations or details!

Related Questions:

1. What is a vertical stretch or compression in transformations?
2. How would the graph change if the equation were $g(x) = \frac{1}{2}|x|$?
3. How can you identify transformations of $|x|$ from its graph?
4. What happens if you add or subtract values inside or outside the absolute value?
5. How would the function look if it were reflected across the x-axis?

Tip:

For vertical stretches, multiplying $|x|$ by a constant $a$ (where $a > 1$) makes the graph steeper. If $0 < a < 1$, it compresses the graph vertically.