Algebra Examples
y=|x-2|-6y=|x−2|−6
Step 1
The parent function is the simplest form of the type of function given.
y=|x|y=|x|
Step 2
Assume that y=|x|y=|x| is f(x)=|x|f(x)=|x| and y=|x-2|-6y=|x−2|−6 is g(x)=|x-2|-6g(x)=|x−2|−6.
f(x)=|x|f(x)=|x|
g(x)=|x-2|-6g(x)=|x−2|−6
Step 3
The transformation from the first equation to the second one can be found by finding aa, hh, and kk for each equation.
y=a|x-h|+ky=a|x−h|+k
Step 4
Factor a 11 out of the absolute value to make the coefficient of xx equal to 11.
y=|x|y=|x|
Step 5
Factor a 11 out of the absolute value to make the coefficient of xx equal to 11.
y=|x-2|-6y=|x−2|−6
Step 6
Find aa, hh, and kk for y=|x-2|-6y=|x−2|−6.
a=1a=1
h=2h=2
k=-6k=−6
Step 7
The horizontal shift depends on the value of hh. When h>0h>0, the horizontal shift is described as:
g(x)=f(x+h)g(x)=f(x+h) - The graph is shifted to the left hh units.
g(x)=f(x-h)g(x)=f(x−h) - The graph is shifted to the right hh units.
Horizontal Shift: Right 22 Units
Step 8
The vertical shift depends on the value of kk. When k>0k>0, the vertical shift is described as:
g(x)=f(x)+kg(x)=f(x)+k - The graph is shifted up kk units.
g(x)=f(x)-kg(x)=f(x)−k - The graph is shifted down kk units.
Vertical Shift: Down 66 Units
Step 9
The sign of aa describes the reflection across the x-axis. -a−a means the graph is reflected across the x-axis.
Reflection about the x-axis: None
Step 10
The value of aa describes the vertical stretch or compression of the graph.
a>1a>1 is a vertical stretch (makes it narrower)
0<a<10<a<1 is a vertical compression (makes it wider)
Vertical Compression or Stretch: None
Step 11
To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.
Parent Function: y=|x|y=|x|
Horizontal Shift: Right 22 Units
Vertical Shift: Down 66 Units
Reflection about the x-axis: None
Vertical Compression or Stretch: None
Step 12
