Answer:
Step-by-step explanation:
The parent function is the simplest form of the type of function given.
y
=
√
x
For a better explanation, assume that
y
=
√
x is f
(
x
)
=
√
x and y
=
√
x is g
(
x
)
=
√
x
.
f
(
x
)
=
√
x
g
(
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
Find a
, h
, and k for y
=
√
x
.
a
=
1
h
=
0
k
=
0
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: None
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: None
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: y
=
√
x
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: None
Vertical Compression or Stretch: None
