Questions: f(x) = x + 3

Transcript text: 2. $f(x)=x+3$

Solution

Solution Steps

To solve the given function transformation problem, we need to identify the type of transformation applied to the base function $ f(x) = x $. The function $ f(x) = x + 3 $ represents a vertical shift of the base function. Specifically, it is shifted upwards by 3 units.

Step 1: Define the Base Function

The base function is given by: \[ f(x) = x \]

Step 2: Define the Transformed Function

The transformed function is given by: \[ f(x) = x + 3 \]

Step 3: Identify the Transformation

The transformation applied to the base function $ f(x) = x $ is a vertical shift. Specifically, the function is shifted upwards by 3 units.

Step 4: Plot the Functions

To visualize the transformation, we plot both the base function and the transformed function. The base function $ f(x) = x $ is a straight line passing through the origin with a slope of 1. The transformed function $ f(x) = x + 3 $ is also a straight line with the same slope but shifted upwards by 3 units.

Final Answer

$\boxed{f(x) = x + 3}$

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