Suppose the graph of $$ f $$ is given. Describe how the graph of the function can be obtained from the graph of $$ f $$. $$ y=7 f(x)-3 $$ a. Stretch the graph of $$ y=f(x) $$ vertically by a factor of 3 , and then shift downward 7 units. b. Reflect the graph of $$ y=f(x) $$ about the $$ y $$-axis, and then shift downward 3 units. c. Stretch the graph of $$ y=f(x) $$ vertically by a factor of 7 , and then shift downward 3 units. d. Stretch the graph of $$ y=f(x) $$ vertically by a factor of 7 , and then shift upward 3 units. e. Stretch the graph of $$ y=f(x) $$ vertically by a factor of 3 , and then shift upward 7 units.

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To analyze the transformation of the function $$ y = 7f(x) - 3 $$ from the graph of $$ f(x) $$, we can break it down into two parts:

1. **Vertical Stretch**: The term $$ 7f(x) $$ indicates that the graph of $$ f(x) $$ is stretched vertically by a factor of 7. This means that every $$ y $$-coordinate of the graph of $$ f(x) $$ is multiplied by 7.

2. **Vertical Shift**: The term $$ -3 $$ indicates that after the vertical stretch, the entire graph is shifted downward by 3 units. This means that every point on the graph of $$ 7f(x) $$ is moved down 3 units.

Putting these two transformations together, we can conclude that the graph of $$ y = 7f(x) - 3 $$ is obtained by stretching the graph of $$ y = f(x) $$ vertically by a factor of 7 and then shifting it downward by 3 units.

Thus, the correct answer is:

**c. Stretch the graph of $$ y=f(x) $$ vertically by a factor of 7, and then shift downward 3 units.**
The graph is stretched vertically by a factor of 7 and then shifted down 3 units.

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