[size=150]In this Geogebra activity, we are studying the effect of geometric transformations on the graph of a function, in this case, [math]f\left(x\right)=x^2[/math].[/size]
[size=150]I[size=100]n the graph below, we have two functions graphed: [br][list][*][math]f\left(x\right)=x^2[/math][br][/*][*][math]g\left(x\right)=x^2+k[/math], where [math]-5\le k\le5[/math][br][/*][/list][/size][/size]
If [math]k>0[/math], what happens to the graph of the function?[br]If [math]k<0[/math], what happens to the graph of the function?
If k is negative, the graph of the function is translated down. [br]If k is positive, the graph of the function is translated up.
Write down the algebraic expression of g(x) in terms of f(x). [br](Hint: We want an equation between g(x) and f(x))
[math]g\left(x\right)=f\left(x\right)+k[/math]
[list][*]If [math]h>0[/math], what happens to the graph of the function?[/*][*]If [math]h<0[/math], what happens to the graph of the function?[/*][/list]
If h is negative, the graph of the function is translated right. [br]If h is positive, the graph of the function is translated left.
Write down the algebraic expression of g(x) in terms of f(x). [br](Hint: We want an equation between g(x) and f(x))
[math]g\left(x\right)=f\left(x-h\right)[/math]