The graph of y=|x|y=∣x∣y, equals, vertical bar, x, vertical bar is reflected across the xxx-axis and then scaled vertically by a factor of \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction. what is the equation of the new graph?

y = - (1/4) |x|

Justification:

The statement is confusing, so I will re-write it to avoid confusions:

"The graph of y=|x| is reflected across the x-axis and then scaled vertically by a factor of 1/4. What is the equation of the new graph? "

Answer

Solution:

1) Reflection acros the x-axis means (a,b) transforms into (a, -b). That is for the given x the reflected function will return the negative of the original value, that is:

y = - |x|

2) Scaling by a factor of 1/4 means that the new function is multiplied by 1/4

=> y = - (1/4) |x| which is the answer