Question

Examine the following graph, where P(x) is the preimage and I(x) is the image after a transformation.

P of X is a cube root function and I of X is the same function translated 4 units to the right.

© 2018 StrongMind. Created using GeoGebra.


Which function correctly describes the transformation?

I(x)=P(x)−4cap i times x is equal to cap p times x minus 4, , ,

I(x)=P(x)+4cap i times x is equal to cap p times x plus 4, , ,

I(x)=P(x+4)cap i times x is equal to cap p times open paren x plus 4 close paren, , ,

I(x)=P(x−4)

Answer 1

the 4th answer I(x) = P(x-4)

Explanation:

the first 2 options are out, because just adding values to the functional result values changes the y value, and the curve is pushed up or down. but not to the side.

just imagine

I(x) = P(x-4) means that the function value of previously at x-4 happens now at x. 4 units "later" (or more to the right).

"x+4" would make the functional value at previously x+4 happen now at x. so, everything would shift to the left (happen "earlier").

therefore, the 4th answer option is correct.