For the given parent function [tex]f(x) =x^{2}[/tex] and the graph of the transformed function [tex]g(x) = x^{2} +k[/tex], slider to change the value of [tex]k[/tex]
- Positive value of [tex]k[/tex] shift the graph above parent function as per the value of [tex]k.[/tex]
- Negative value of [tex]k[/tex] shift the graph below the parent function as per the value of [tex]k.[/tex]
What is function?
" Function is defined as the relation between the variables such that for each input value there exist exactly one output."
According to the question,
Given parent function,
[tex]f(x) =x^{2}[/tex]
Transformed function
[tex]g(x) = x^{2} +k[/tex]
As shown in the drawn graph
- Positive value of k shift the graph above parent function.
Consider
[tex]k=1[/tex]
[tex]g(x) = x^{2} +1[/tex]
Here , transformed function graph shift by one unit above parent function.
- Negative value of k shift the graph below parent function.
- Consider
- [tex]k=-1[/tex]
- [tex]g(x) = x^{2} -1[/tex]
- Here ,
- transformed function graph
- shift by one unit below
- parent function
- .
Hence, for the given parent function [tex]f(x) =x^{2}[/tex] and the graph of the transformed function [tex]g(x) = x^{2} +k[/tex], slider to change the value of [tex]k[/tex]
- Positive value of [tex]k[/tex] shift the graph above parent function as per the value of [tex]k.[/tex]
- Negative value of [tex]k[/tex] shift the graph below the parent function as per the value of [tex]k.[/tex]
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