Question

If the parent function f(x) = |x| is transformed to g(x) = |x + 5|, what transformation occurs from f(x) to g(x)?

Answer 1

The transformation that occurs from f(x) to g(x) is the graph of f(x) is shifted to the left to create g(x).

What transformation occurs from f(x) to g(x)?

The equations of the functions are given as

f(x) = |x|

g(x) = |x + 3|

The above implies that

g(x) = f(x + 3)

When a function is shifted to the left by h units, it is represented as

g(x) = f(x + h)

This means that

h = 3

So, the transformation that occurs from f(x) to g(x) is the graph of f(x) is shifted to the left to create g(x).

Hence, the required transformation that occurs from f(x) to g(x) is the graph of f(x) is shifted to the left to create g(x).

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