Question

How are the functions y = 4x and y = -4x + 3 related? Select all that apply.The graph of y = 4x is reflected in the x-axis and translated up 3 units.Each output is the opposite of y = 4x plus 3 additional units.The graph of y = 4x is reflected in the y-axis and translated down 3 units.The lines are perpendicular to each other.The lines are parallel to each other.

Answer 1

Answer:

Choice 1 and Choice 2.

Explanation:

First let us consider, y = 4x and y = -4x. This translation suggests

$y\rightarrow-y$

which is a reflection across the x-axis.

Next, adding 3 to y = -4x, shifts the reflected line by 3 up the y-axis. Therefore, choice 1 is correct.

Another way to think about this is that after translation, the output of y = 4x is opposite of y - 4x (because a negative sign is involved ), and y = -4x + 3 can be thought of as adding 3 units to y = -4x; therefore, choice 2 is also correct.