What transformations produce the graph of from the graph of the parent function ? Select all that apply. (1 point)
reflection over the x-axis
reflection over the y-axis
horizontal shift to the left 2 units
horizontal shift to the right 2 units
vertical shift up 2 units
vertical shift down 2 units
The correct transformations that produce the graph are:
- Reflection over the x-axis
- Reflection over the y-axis
- Horizontal shift to the left 2 units
- Vertical shift up 2 units
To determine the transformations that produce the graph of a function from the parent function, we can analyze the given options.
1. Reflection over the x-axis: This transformation would flip the graph upside down.
2. Reflection over the y-axis: This transformation would mirror the graph horizontally.
3. Horizontal shift to the left 2 units: This transformation would move the graph 2 units to the left.
4. Horizontal shift to the right 2 units: This transformation would move the graph 2 units to the right.
5. Vertical shift up 2 units: This transformation would shift the graph 2 units upwards.
6. Vertical shift down 2 units: This transformation would shift the graph 2 units downwards.
Therefore, the transformations that produce the graph of the parent function include:
- Reflection over the x-axis
- Reflection over the y-axis
- Horizontal shift to the left 2 units
- Horizontal shift to the right 2 units
- Vertical shift up 2 units
- Vertical shift down 2 units.
To determine which transformations produce the graph of the function, we need to understand each transformation and how it affects the parent function.
1. Reflection over the x-axis: This transformation flips the graph vertically. All positive y-values become negative, and all negative y-values become positive.
2. Reflection over the y-axis: This transformation flips the graph horizontally. All positive x-values become negative, and all negative x-values become positive.
3. Horizontal shift to the left 2 units: This transformation moves the graph to the left by shifting each point 2 units to the left. To achieve this, subtract 2 from each x-coordinate.
4. Horizontal shift to the right 2 units: This transformation moves the graph to the right by shifting each point 2 units to the right. To achieve this, add 2 to each x-coordinate.
5. Vertical shift up 2 units: This transformation moves the graph upward by shifting each point 2 units up. To achieve this, add 2 to each y-coordinate.
6. Vertical shift down 2 units: This transformation moves the graph downward by shifting each point 2 units down. To achieve this, subtract 2 from each y-coordinate.
Now, let's analyze each option:
- Reflection over the x-axis: This is a valid transformation that results in the graph of the function. It flips the graph vertically, changing the signs of the y-values.
- Reflection over the y-axis: This is a valid transformation that results in the graph of the function. It flips the graph horizontally, changing the signs of the x-values.
- Horizontal shift to the left 2 units: This is a valid transformation that results in the graph of the function. It shifts the graph to the left by subtracting 2 from each x-coordinate.
- Horizontal shift to the right 2 units: This is a valid transformation, but it does not produce the graph of the function. It would shift the graph to the right by adding 2 to each x-coordinate, resulting in a different graph.
- Vertical shift up 2 units: This is a valid transformation that results in the graph of the function. It shifts the graph upward by adding 2 to each y-coordinate.
- Vertical shift down 2 units: This is a valid transformation, but it does not produce the graph of the function. It would shift the graph downward by subtracting 2 from each y-coordinate, resulting in a different graph.
Therefore, the correct transformations that produce the graph of the function are:
- Reflection over the x-axis
- Reflection over the y-axis
- Horizontal shift to the left 2 units
- Vertical shift up 2 units
It's worth noting that these transformations can be combined to create more complex transformations.