What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units?

Given:

The parent function is

We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.

Shift left 9 units:

The rule to shift the graph c units to the left is given by

where c is the positive real number.

Hence, to shift the graph 9 units to the left is given by

Vertical stretch by a factor of 4:

The rule to stretch the graph vertically by a factor of c is given by

where

Hence, to stretch the graph vertically by a factor of 4, we have;

Shifting 5 units up:

The rule to shift the graph c units upward is given by

where c is the positive real number.

Hence, to shift the graph 5 units upward is given by

Therefore, the function is created from the graph by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.

Hence, the graph g(x) is

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