https://file.aiquickdraw.com/mathbot/file/1727872027495hge8vbpc.jpg

The graph of y, equals, f, of, xy=f(x) is the solid black graph below. Which function represents the dotted graph?
x
y
Answer
Multiple Choice Answers
y, equals, f, of, x, minus, 4, plus, 4y=f(x−4)+4
y, equals, f, of, x, plus, 4, plus, 4y=f(x+4)+4
y, equals, f, of, x, plus, 4, minus, 4y=f(x+4)−4
y, equals, f, of, x, minus, 4, minus, 4y=f(x−4)−4

11th grade math accurate answer 2024

From the graph provided, we have two parabolas. The solid black graph represents the function \( y = f(x) \), and the dotted graph is a transformation of this function. Let's analyze the transformation:

1. **Horizontal Translation**: The dotted graph is shifted to the left compared to the solid graph, which indicates a horizontal translation.
   
2. **Vertical Translation**: The dotted graph is also shifted downward, suggesting a vertical translation.

The transformation rules are:
- Horizontal shifts: If the graph shifts left by \( a \), it is represented by \( f(x + a) \).
- Vertical shifts: If the graph shifts down by \( b \), it is represented by \( f(x) - b \).

By observing the graph:
- The dotted graph has been shifted 4 units to the left.
- The dotted graph has also been shifted 4 units down.

Therefore, the correct function representing the dotted graph is:
\[
y = f(x + 4) - 4
\]

This corresponds to the third option: \( y = f(x+4) - 4 \).

### Would you like further explanation on function transformations?

Here are five follow-up questions related to this concept:
1. What happens if you shift the graph \( f(x) \) to the right instead of the left?
2. How does a vertical stretch or compression affect the graph of \( f(x) \)?
3. How would the equation change if the graph were shifted upwards instead of downwards?
4. Can you describe how a reflection over the x-axis would affect \( f(x) \)?
5. How would both a horizontal stretch and vertical stretch affect the graph of \( f(x) \)?

### Tip:
To quickly identify horizontal shifts, remember that moving left corresponds to \( f(x + a) \), while moving right corresponds to \( f(x - a) \).

The graph of y = f(x) is the solid black graph below. Which function represents the dotted graph?

Analyze a graph transformation problem involving horizontal and vertical shifts. This example covers key concepts in quadratic functions and transformations, helping students in Grade 11 understand how to modify function graphs.

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