Question

Question 2 A) Use the image to answer the question. Interpret the key features of the graph to determine the transformation that occurred from its original function y=x−−√3y=x3. (1 point) Responses This graph represents a shift up due to the change in the y-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 down due to the change in the y-intercept from the parent function. This graph represents a shift down 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 to the right due to the change in the x -intercept from the parent function. This graph represents a shift to the left due to the change in the x-intercept from the parent function.

Graph:
(-11,-2)
(-4,-1)
(-3,0)
(-2,1)
(5,2)

Answer 1

To analyze the transformation from the original functions \( y = \sqrt{x} \) and \( y = x^3 \), we can look at the points given in the graph:
- (-11, -2)
- (-4, -1)
- (-3, 0)
- (-2, 1)
- (5, 2)

1. **Understanding the Parent Functions**:
- The graph of \( y = \sqrt{x} \) starts from the origin (0,0) and increases as \( x \) increases for \( x \geq 0 \).
- The graph of \( y = x^3 \) passes through the origin (0,0) as well and is an increasing function for all real numbers.

2. **Shifts and Transformations**:
- If the new graph is derived from either parent function, we should identify how the y-values of the points provided in the graph relate to the corresponding points of the parent function.

3. **Determining the Transformation**:
- The first point (-3, 0) does not directly correspond to any point on y = √x or y = x³, since these functions are not defined for negative x-values.
- The y-value at (-2, 1) suggests that we have a shift up, especially since the y-intercept appears to be elevated based on the values of y provided.
- There might be an addition of a constant that shifts the graph up (or down) from the original function.

Without the actual visual representation of the graph, I cannot pinpoint the exact nature (up or down) of the shift. However, if we consider typical shifts in terms of transformations:

Based on the gathered insight, **a potential interpretation based on y-values indicates an upward shift of the function.**

Accordingly, the most likely transformation is that **the graph represents a shift up due to the change in the y-intercept from the parent function.**

Thus, the correct response is: **This graph represents a shift up due to the change in the y-intercept from the parent function.**