Final answer:
The transformation that moves the y-intercept to (0,4) is a vertical translation of 4 units up. This is because this transformation adds 4 to the y-value of every point on the graph. (option d is the correct answer).
Step-by-step explanation:
To determine the transformation that results in a y-intercept of (0,4), we need to analyze how various transformations affect the position of the y-intercept. The original function has a y-intercept at (0,0). The given options are:
Reflection over the x-axis: This transformation would change the sign of the y-coordinate, but it wouldn't alter the y-intercept's vertical position.
Vertical stretch by a factor of 2: Vertical stretching would change the function's shape, but it wouldn't affect the y-intercept's location.
Translation 3 units to the right: This transformation would affect the x-intercept, not the y-intercept.
Vertical translation 4 units up A vertical translation by a constant, in this case, 4 units up, would shift the entire function vertically. This would indeed result in a new y-intercept at (0,4).
Therefore, the correct transformation is option d) Vertical translation 4 units up.
To achieve a y-intercept of (0,4), the function needs to undergo a vertical translation of 4 units upward.