Question

Describe the transformations of f(x) when compared to the parent function [y = x2].
f(x) = x2+5

Answer 1

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

Answer 2

The transformations of f(x) when compared to the parent function is the graph of $f(x)=x^2+5$ is moved 5 units up

Transformation of functions

Transformation of function is transforming a function from one form to another form .

Rules of transformation :

f(x)-> f(x)+a , f(x) will be moved 'a' units up

f(x)-> f(x)-a , f(x) will be moved 'a' units down

f(x)-> f(x-a) , f(x) will be moved 'a' units right

f(x)-> f(x+a) , f(x) will be moved 'a' units left

f(x)-> -f(x), f(x) will be reflected across x-axis

f(x)-> f(-x), f(x) will be reflected across y-axis

For quadratic, the parent function is $f(x)=x^2$

Given that $f(x)=x^2+5$

Here , 5 is added with f(x) at the end

f(x)-> f(x)+a , f(x) will be moved 'a' units up

$f(x)=x^2 ------ > f(x) =x^2+5$

The graph of f(x) will be move 5 units up

the transformations of f(x) when compared to the parent function is the graph is moved 5 units up

Learn more about transformation here:

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