<u>Given</u>:
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.
<u>Shift left 9 units:</u>
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
<u>Vertical stretch by a factor of 4:</u>
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;
<u>Shifting 5 units up:</u>
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