Question

Question 2: Consider the relationship between y=f(x) and y=-f(x)
Part A fill in the blanks (3 points):
What is this type of function transformation called? What does it look like on a graph?
Answer: This type of transformation is called a [blank]. Specifically, it is a reflection over the [blank]-axis. On a graph, this means that every point on the graph of y=-f(x) [blank].
Part B Sketch a graph ( 7 points):
Choose one of the parent functions (. Create a fake graph for both the parent function and the transformation. Be sure to clearly label each sketch.
F(x)= 3√x
F (x) = 2^x
F (x) = x
f(x)= x^2
F (x) = √x

Answer 1

### Part A: Fill in the Blanks

1. **What is this type of transformation called?**
- Answer: This type of transformation is called a **reflection**.

2. **What does it look like on a graph?**
- Answer: Specifically, it is a reflection over the **x-axis**. On a graph, this means that every point on the graph of y = -f(x) **is mirrored across the x-axis**.

---

### Part B: Sketch a Graph

Let's choose the parent function \( f(x) = x^2 \) for the graph illustrations.

### Graph Sketches

#### Parent Function: \( f(x) = x^2 \)

1. **Description**: The graph of \( f(x) = x^2 \) is a parabola that opens upward with its vertex at the origin (0,0).

- Sketch:
```
|
4| *
| * *
3| * *
| * *
2| * *
| * *
1| * *
| * *
---- +------------------------------
-2 -1 0 1 2 3 4
```

---

#### Transformation: \( g(x) = -x^2 \)

2. **Description**: The graph of \( g(x) = -x^2 \) is also a parabola, but it opens downward with its vertex at the origin (0,0).

- Sketch:
```
|
4|
|
3|
|
2|
|
1|
| * *
---- +------------------------------
-2 -1 0 1 2 3 4
| * *
-1| * *
| * *
-2| * *
| *
-3| *
|
-4|
```

### Labeling
- **Curve for \( f(x) = x^2 \)**: Label this curve as "Parent Function: \( f(x) = x^2 \)".
- **Curve for \( g(x) = -x^2 \)**: Label this curve as "Transformation: \( g(x) = -x^2 \)".

### Conclusion
The sketches show the effect of reflecting the parent function \( f(x) = x^2 \) across the x-axis to create the function \( g(x) = -x^2 \).