Duplicate Question
The question on this page has been marked as a duplicate question.
Original 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 fun...Question
Question 3: 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 from question 1.(F(x)= 3√x
F (x) = 2^x
F (x) = x
f(x)= x^2
F (x) = √x
)create a full graph. both the parent function and the transformation. Be sure to clearly label each sketch.
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 from question 1.(F(x)= 3√x
F (x) = 2^x
F (x) = x
f(x)= x^2
F (x) = √x
)create a full graph. both the parent function and the transformation. Be sure to clearly label each sketch.
Answers
GPT-4o mini
**Part A: Fill in the blanks**
This type of transformation is called a **horizontal reflection**. Specifically, it is a reflection over the **y-axis**. On a graph, this means that every point on the graph of y = f(-x) **is mirrored** across the y-axis relative to the graph of y = f(x).
---
**Part B: Sketch a graph**
Let's choose the parent function \( f(x) = x^2 \) (the quadratic function) for this part.
1. **Graph of the Parent Function \( f(x) = x^2 \)**:
- The parent function is a parabola opening upwards with its vertex at the origin (0, 0).
- Points to plot:
- (0, 0)
- (1, 1)
- (2, 4)
- (-1, 1)
- (-2, 4)
2. **Graph of the Transformation \( f(-x) = (-x)^2 = x^2 \)**:
- The transformation \( f(-x) \) results in the exact same graph as the parent function because the parabola is symmetric about the y-axis.
**Sketch Description**:
- Draw a coordinate plane with the x-axis and y-axis labeled.
- Plot the points for \( f(x) = x^2 \).
- Since the graph of \( f(-x) = x^2 \) is the same as \( f(x) \), it will overlap exactly.
- Label the graph of \( f(x) = x^2 \) as the "Parent Function" and the graph of \( f(-x) \) also as "Transformed Function".
**Final Note**: Both functions will look the same in this case, as the quadratic function is symmetric about the y-axis.
This type of transformation is called a **horizontal reflection**. Specifically, it is a reflection over the **y-axis**. On a graph, this means that every point on the graph of y = f(-x) **is mirrored** across the y-axis relative to the graph of y = f(x).
---
**Part B: Sketch a graph**
Let's choose the parent function \( f(x) = x^2 \) (the quadratic function) for this part.
1. **Graph of the Parent Function \( f(x) = x^2 \)**:
- The parent function is a parabola opening upwards with its vertex at the origin (0, 0).
- Points to plot:
- (0, 0)
- (1, 1)
- (2, 4)
- (-1, 1)
- (-2, 4)
2. **Graph of the Transformation \( f(-x) = (-x)^2 = x^2 \)**:
- The transformation \( f(-x) \) results in the exact same graph as the parent function because the parabola is symmetric about the y-axis.
**Sketch Description**:
- Draw a coordinate plane with the x-axis and y-axis labeled.
- Plot the points for \( f(x) = x^2 \).
- Since the graph of \( f(-x) = x^2 \) is the same as \( f(x) \), it will overlap exactly.
- Label the graph of \( f(x) = x^2 \) as the "Parent Function" and the graph of \( f(-x) \) also as "Transformed Function".
**Final Note**: Both functions will look the same in this case, as the quadratic function is symmetric about the y-axis.