Question

The parent function f(x) = x3 is transformed to g(x) = (x - 1)3 + 4. Identify the graph of g(x).

Answer 1

Start with $f(x) = x^3$

First transformation: $h(x) = (x-1)^3$

Type of transformation: $f(x)\mapsto f(x+k)$

Effect: Every time you add a constant to the function argument, you translate its graph horizontally, k units to the left if k is positive, k units to the right if k is negative.

Second transformation: $g(x) = (x-1)^3+4$

Type of transformation: $f(x)\mapsto f(x)+k$

Effect: Every time you add a constant to the function, you translate its graph vertically, k units upwards if k is positive, k units downward if k is negative.

So, starting from the parent function, you translate its graph 1 unit right and 4 units up, and you have the graph of g(x).