Questions: Suppose the graph below left is the function f(x). In the space below, describe what transformations are occurring in the transformed function 3f(x)+1. Then graph it on the coordinate plane below right. (4 points)

Suppose the graph below left is the function f(x). In the space below, describe what transformations are occurring in the transformed function 3f(x)+1. Then graph it on the coordinate plane below right. (4 points)

Transcript text: Suppose the graph below left is the function $f(x)$. In the space below, describe what transformations are occuring in the transformed function $3 f(x)+1$. Then graph it on the coordinate plane below right. (4 points)

Solution

Solution Steps

Step 1: Identify the Original Function

The original function $ f(x) $ is given by the graph on the left. We need to understand its key features such as intercepts, maxima, minima, and intervals of increase and decrease.

Step 2: Determine the Transformations

The transformed function is $ 3f(x) + 1 $. This involves two transformations:

Vertical Stretch: The function $ f(x) $ is stretched vertically by a factor of 3.
Vertical Shift: The function is then shifted upward by 1 unit.

Step 3: Apply the Transformations to Key Points

Apply the transformations to key points of the original function:

For any point $(x, y)$ on $ f(x) $, the corresponding point on $ 3f(x) + 1 $ will be $(x, 3y + 1)$.

Final Answer

The graph of the transformed function $ 3f(x) + 1 $ will be a vertically stretched version of the original graph by a factor of 3, and then shifted upward by 1 unit.

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