Question
Which is the graph of the parent function f(x) = |x|
Answers
GPT-4o mini
The graph of the parent function \( f(x) = |x| \) is a V-shaped graph that opens upwards. Here are some key characteristics of the graph:
1. **Vertex**: The vertex of the graph is at the origin (0, 0).
2. **Symmetry**: The graph is symmetric with respect to the y-axis, which means that if you fold the graph along the y-axis, both halves will match.
3. **Quadrants**: The graph is located in the first and second quadrants. It consists of two linear segments:
- For \( x < 0 \), \( f(x) = -x \) (a line with a slope of -1).
- For \( x \geq 0 \), \( f(x) = x \) (a line with a slope of 1).
4. **Intercepts**: The graph intersects the y-axis at (0, 0).
To sketch the graph:
- Plot points such as (-2, 2), (-1, 1), (0, 0), (1, 1), and (2, 2).
- Connect these points to form the V-shape.
This visual representation helps to easily identify the characteristics of the absolute value function \( f(x) = |x| \).
1. **Vertex**: The vertex of the graph is at the origin (0, 0).
2. **Symmetry**: The graph is symmetric with respect to the y-axis, which means that if you fold the graph along the y-axis, both halves will match.
3. **Quadrants**: The graph is located in the first and second quadrants. It consists of two linear segments:
- For \( x < 0 \), \( f(x) = -x \) (a line with a slope of -1).
- For \( x \geq 0 \), \( f(x) = x \) (a line with a slope of 1).
4. **Intercepts**: The graph intersects the y-axis at (0, 0).
To sketch the graph:
- Plot points such as (-2, 2), (-1, 1), (0, 0), (1, 1), and (2, 2).
- Connect these points to form the V-shape.
This visual representation helps to easily identify the characteristics of the absolute value function \( f(x) = |x| \).