Is Vertical Compression Correctly Applied in This Function Transformation?

[dragon513]

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

 

[HallsofIvy]

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

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.