Question

Which of the following statements is true about vertical transformations of linear functions?A)The resulting functions will all have the same slope.B)The graphs of linear function and its vertical transformation will intersect at only one point.C)The original function and the transformed function will have the same equations but different graphs.D)Vertical transformations do not apply to equations of the form y= b.

Answer 1

The vertical transformation of a linear function of the form

`y=mx+b`

is the shift of the y-intercept b; meaning, the vertical transformation only changes the value of b and leaves the slope unchanged.

Hence, the vertical transformation of functions leaves the slope unchanged, meaning choice A is correct one

Just to make sure we have got the right answer let us probe other answer choices.

Choice B is not correct since it implies that parallel lines should meet.

Choice C is not correct since the value of b is changed in the transformation, and therefore, the original equation and the transformed equation are not the same.

The function y = b is also a linear function but with slope zero and changing b here also counts as a vertical transformation - so this choice D is wrong.