Describe the transformation of f(x)=x^2 represented by g. g(x) = (x-5)^2+3

Question

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Answer 1

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

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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

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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