Polynomials (1 Viewer)

[xwrathbringerx]

Describe how the graph of f(x) = x^3 can be transformed into the graph of f(x) = (x+3)^3 and f(x) = (x+3)^3 - 2.

Could someone please explain how to do this? The textbook didn't provide an example.

 

[Revacious]

consider f(x) = x^2

then f(x+a) is (x-a)^2, which ahs its vertex at (a,0)

therefore when x is replaced with (x-a), you shift the curve a units to the right.


by adding a constant at the end, ie f(x) = x^2 + c, youre shifting it c units upwards.

 

[annabackwards]

Adding to what Revacious said:

f(x) = (x+3)^3
is just the graph f(x) = x^3 translated 3 units to the left

And f(x) = (x+3)^3 - 2
is just the graph f(x) = x^3 translated 3 units to the left and shifted down 2 units