Use the graph of y fx to graph the function y3 4fx 3 Labe

Use the graph of y = f(x) to graph the function y=3 - 4f(x - 3). Label the points on the sketch. For each point on the graph of f(x), compute the location of the corresponding point on the graph of

Solution

y = f(x)

y = 3 - 4f(x- 3)>this is obtained after following transformations:

i) shift f(x) horizontalyy by 3 units to right by 3 units (-3, -2) ----> ( -3+3 , -2) = ( 0 , -2)

ii) stretch vertically f(x -3) by 4 units ----> 4f(x -3) : ( 0, -2) ---->( 0, -8)

iii) reflect along x axis ----> -4f(x -3) : ( 0, 8)

iv) shift -4f(x -3) vertically up by 3 units : 3 - 4f(x-3) : ( 0, 11)

Similarly (-1 , -1) ----> ( 2 , 7)

( 0, 0) -----> ( 3 , 3)

( 1 , 1) ------> ( 4 , -1)

( 2 , -1) -----> ( 5 , 7)

Graph of Option A seems to have the points above