Absolute Values

Question

Let f(x)= |𝑥|where x can be any real number. Write a formula for the function whose graph is the transformation of the graph of f given by the instructions below:

a. A translation left 5 units and up 3 units: ________________________________________

b. A translation right 1 units and down 3 units: _____________________________________

c. A vertical stretch by a factor of ½ and translation up 5 units: ________________________

Answer 1

Transformations of equations are:

horizontal shift right |x-5|

Left |x+5|

vertical shift up. |x| +5

down |x|-5

compression vertically 5|x|

stretch vertically 1/5|X|

compression horizontally |5x|

compression vertically |1/5x|

flip over x axis. -|x|

Over y axis. |-x|

1. left 5 and up 3 f(x)= |x+5| +3
2. Right 1 down 3 f(x)= |x+1| -3
3. vertical stretch by 1/2 up 5 f(x)= 1/2|x| +5