Final answer:
The transformation of the linear parent function to create g(x) = -5x + 1 involves a reflection across the x-axis (due to the negative slope) and a vertical translation up by 1 unit (due to the +1), resulting in a steeper slope and an upward shift.
Step-by-step explanation:
The transformations that occurred to the linear parent function to create g(x) = -5x + 1 are: a reflection across the x-axis due to the negative sign in front of 5, which indicates that the slope is negative and therefore the graph slopes downwards, and a vertical translation upward by 1 unit due to the +1 at the end of the equation.
The correct transformation options are therefore a reflection across the x-axis, making the slope steeper, and a translation vertically up by 1 unit. So the correct answer to the question of transformation would be c) Steeper slope, due to the multiplier of -5 and a) Translation up by 1 unit, due to the +1. There is no translation left or right since the y-intercept is +1 and there is no change in the slope's sign apart from the reflection.