f(x)=|x| is the parent function. Let y= the transformed function. Describe how to obtrain the graph of y (below) from the graph of f(x). Graph both functions to verify your answer. y=|x-3|-3

The graph above shows both functions:

- The dashed blue line represents the parent function \( f(x) = |x| \), which is a V-shaped graph with its vertex at \( (0, 0) \).
- The red line represents the transformed function \( y = |x - 3| - 3 \), which has been shifted 3 units to the right and 3 units downward, with its vertex at \( (3, -3) \).

These shifts confirm the transformations described earlier.

Do you have any questions or would you like more details?

Here are 5 related questions to deepen your understanding:
1. How would the graph change if the function was \( y = |x + 3| - 3 \)?
2. What happens if we add a coefficient to the absolute value, like \( y = 2|x - 3| - 3 \)?
3. Can you describe the effect of \( y = |x - 3| + 3 \) on the graph?
4. How would a reflection over the x-axis look in an absolute value function?
5. What is the effect of a vertical stretch or compression on \( y = |x| \)?

**Tip:** Horizontal shifts are counterintuitive—if you subtract a value from \( x \), the graph shifts to the right.

f(x) = |x| is the parent function. Let y = the transformed function. Describe how to obtain the graph of y (below) from the graph of f(x). Graph both functions to verify your answer. y = |x - 3| - 3.

Learn how to graphically transform the absolute value function f(x) = |x| to y = |x - 3| - 3. This tutorial covers key transformations such as horizontal shifts and vertical shifts, and includes both graph representations for a visual understanding. Suitable for high school students.

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