The parent function is the simplest form of the type of function given.
f(x)=x^2
The transformation being described is from f(x)=x^2
to g(x)=(x−5)^2+3
******************************************************************************
By definition,
.
f(x)=x^2→g(x)=(x−5)^2+3
The horizontal shift depends on the value of h. 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.
Hence, in the question above, Horizontal Shift: Right 5 Units
The vertical shift depends on the value of k. 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.
Therefore, in the question above, Vertical Shift: Up 3 Units
The graph is reflected about the x-axis when g(x)=−f(x)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when g(x)=f(−x)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of 'a'
.
When 'a' is greater than 1 : Vertically stretched
When 'a' is between 0 and 1 : Vertically compressed
Vertical Compression or Stretch: None
****************************************************************************
Comparing and listing the transformations as follows:
Parent Function: f(x)=x^2
Horizontal Shift: Right 5 Units
Vertical Shift: Up 3 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
