Question
Interpret the key features of the graph to determine the transformation that occurred from its
original function y =
3
√x.
(1 point)
This graph represents a shift to the left due to the change in the x-intercept from the parent function.
This graph represents a shift up due to the change in the y-intercept from the parent function.
This graph represents a shift to the right due to the change in the x-intercept from the parent
function.
This graph represents a shift down due to the change in the y-intercept from the parent function.
original function y =
3
√x.
(1 point)
This graph represents a shift to the left due to the change in the x-intercept from the parent function.
This graph represents a shift up due to the change in the y-intercept from the parent function.
This graph represents a shift to the right due to the change in the x-intercept from the parent
function.
This graph represents a shift down due to the change in the y-intercept from the parent function.
Answers
Answered by
GPT-4o mini
To accurately interpret the key features of the graph of the function \( y = \sqrt[3]{x} \) (or \( y = 3\sqrt{x} \)), we need to first establish the characteristics of the original function and how they change based on transformations.
The function \( y = \sqrt[3]{x} \) is the parent function, which passes through the origin (0,0). When a transformation occurs, we can track how the graph changes in terms of shifts (left/right/up/down) or by simple stretches/compressions.
1. **Shift Left/Right:** If the graph is modified to \( y = \sqrt[3]{x + c} \), this would represent a shift to the left if \( c > 0 \) (adding a positive value inside the function) or to the right if \( c < 0 \).
2. **Shift Up/Down:** If the graph is modified to \( y = \sqrt[3]{x} + k \), this would represent a shift up if \( k > 0 \) (adding a positive number outside the function) or down if \( k < 0 \).
Since no specific transformation is given in your question, here’s how to select the correct interpretation based on options provided:
- **Shift Left:** Refers to moving the graph left-side of the original position.
- **Shift Right:** Refers to moving the graph right-side of the original position.
- **Shift Up:** Refers to moving the graph higher on the y-axis.
- **Shift Down:** Refers to bringing the graph lower on the y-axis.
Without additional information, I can't definitively pinpoint the shifts based only on the description given, as the transformations of the graph can radically change its intercepts and overall position.
In conclusion, based on your options:
1. If the x-intercept has changed and the graph has moved left, then **"This graph represents a shift to the left due to the change in the x-intercept from the parent function."** could be correct.
2. If it has moved up, then **"This graph represents a shift up due to the change in the y-intercept from the parent function."** would be accurate.
3. A rightward shift would imply a different interpretation and similarly for downward shifts.
Without the specific graph or alteration details, I recommend looking at how the critical points and intercepts have changed from \( y = \sqrt[3]{x} \) to the transformed version to select the most accurate description from the choices given.
The function \( y = \sqrt[3]{x} \) is the parent function, which passes through the origin (0,0). When a transformation occurs, we can track how the graph changes in terms of shifts (left/right/up/down) or by simple stretches/compressions.
1. **Shift Left/Right:** If the graph is modified to \( y = \sqrt[3]{x + c} \), this would represent a shift to the left if \( c > 0 \) (adding a positive value inside the function) or to the right if \( c < 0 \).
2. **Shift Up/Down:** If the graph is modified to \( y = \sqrt[3]{x} + k \), this would represent a shift up if \( k > 0 \) (adding a positive number outside the function) or down if \( k < 0 \).
Since no specific transformation is given in your question, here’s how to select the correct interpretation based on options provided:
- **Shift Left:** Refers to moving the graph left-side of the original position.
- **Shift Right:** Refers to moving the graph right-side of the original position.
- **Shift Up:** Refers to moving the graph higher on the y-axis.
- **Shift Down:** Refers to bringing the graph lower on the y-axis.
Without additional information, I can't definitively pinpoint the shifts based only on the description given, as the transformations of the graph can radically change its intercepts and overall position.
In conclusion, based on your options:
1. If the x-intercept has changed and the graph has moved left, then **"This graph represents a shift to the left due to the change in the x-intercept from the parent function."** could be correct.
2. If it has moved up, then **"This graph represents a shift up due to the change in the y-intercept from the parent function."** would be accurate.
3. A rightward shift would imply a different interpretation and similarly for downward shifts.
Without the specific graph or alteration details, I recommend looking at how the critical points and intercepts have changed from \( y = \sqrt[3]{x} \) to the transformed version to select the most accurate description from the choices given.