Answer:
Step-by-step explanation:
The parent function is the simplest form of the type of function given.
f(x)=√x
The transformation from the first equation to the second one can be found by finding a
, h, and k
for each equation.
y=a√x−h+k
Factor a 1
out of the absolute value to make the coefficient of x equal to 1
.
y=√x
Factor a 1
out of the absolute value to make the coefficient of x equal to 1
.
y=√x−3+2
Find a
, h, and k for y=√x−3+2
.
a=1
h=3
k=2
The horizontal shift depends on the value of h
. When h>0
, the horizontal shift is described as:
g(x)=f(x+h)
- The graph is shifted to the left h
units.
g(x)=f(x−h)
- The graph is shifted to the right h
units.
Horizontal Shift: Right 3
Units
The vertical shift depends on the value of k
. When k>0
, the vertical shift is described as:
g(x)=f(x)+k
- The graph is shifted up k
units.
g(x)=f(x)−k
- The graph is shifted down k
units.
Vertical Shift: Up 2
Units
The sign of a
describes the reflection across the x-axis. −a
means the graph is reflected across the x-axis.
Reflection about the x-axis: None
The value of a
describes the vertical stretch or compression of the graph.
a>1
is a vertical stretch (makes it narrower)
0<a<1
is a vertical compression (makes it wider)
Vertical Compression or Stretch: None
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: f(x)=√x
Horizontal Shift: Right 3
Units
Vertical Shift: Up 2
Units
Reflection about the x-axis: None
Vertical Compression or Stretch: None
