The discussion centers on the application of vertical compression in the function transformation of f(x) = 2(x^2) - 4. The correct transformation results in g(x) = (x^2) - 2 after applying a vertical compression by a factor of 1/2. The initial confusion arises from a misunderstanding of how vertical changes affect the output of the function. The solution confirms that the vertical compression modifies the entire output value, leading to the new equation.
PREREQUISITESStudents learning algebra, educators teaching function transformations, and anyone seeking to clarify concepts related to vertical compression in quadratic equations.
No, the book's solution is correct. Horizontal changes are changes in x, vertical changes are changes in y. Since this is a vertical compression by 1/2, first calculate y= 2x2- 4, the calculate (1/2)y= (1/2)(2x2- 4)= x2- 2 (becareful to use the "distributive law"- multiply both parts by 1/2). The new y is y= x2- 2.dragon513 said:Q. Given f(x)=2(x^2)-4 , determine the new equation g(x) after a vertical compression by a factor of 1/2.
The answer provided by the book is g(X) = (x^2)-2, but shouldn't it be g(x) = (x^2)-4 ?
Help will be much appreciated.
Regards,
Adam