Graph f(x)

Question

How can the graph f(x)=0.3|x-6|+7 be obtained from the graph of y=|x|?

 

a) Shift it horizontally 3 units to the left. Shrink it vertically by a factory of 0.6. Shift it 7 units upward

b) Shift it horizontally 6 units to the left. Stretch it vertically by a factor of 3. Shift it 7 units upward.

c) Shift it horizontally 7 units to the right. Stretch it vertically by a factor of 3. Shift it 6 units downward. 

d) Shift it horizontally 6 units to the right. Shrink it vertically by a factor of 0.3. Shift id 7 units upward. 

Answer 1

For a function y=f(x) and a positive constant c:

1. y=f(x+c) shifts the graph of f(x) c units to the left, f(x-c) shifts f(x) c units to the right
2. y = c*f(x) stretches the graph vertically; y = (1/c)f(x) compresses the graph vertically
3. y = f(x) + c shifts the graph up c units; y = f(x) - c shifts it down c units.

 

For your problem, f(x) = |x|, so:

 

f(x+c) = |x+c|

(1/c)*f(x) = (1/c)*|x|

f(x)+c = |x| + c