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Pre calculus: transformations of functions

Pre calculus: transformations of functions-example-1

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The parent function is f(x) = |x|

The transformed function is f(x) = -1/2|x| + 3

The parent function is f(x) = x²

The description of the transformation is reflection across the y-axis followed by a vertical compression by 2, a translation right by 1 unit and a translation up by 2 units

Identifying the parent function

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we can see that

The function on the graph is made of two independent linear function with the same origin

This means that the parent is an absolute value function and can be represented as f(x) = |x|

Identifying the transformed function

Here, we have

Vertical compression by 1/2

So, we get

f(x) = 1/2|x|

Reflection over the x-axis gives

f(x) = -1/2|x|

A translation up by 3 units gives

f(x) = -1/2|x| + 3

So, the transformed function is f(x) = -1/2|x| + 3

Identifying the parent function

Here, we have

f(x) = -2(x - 1)² + 2

The parent is a quadratic function and can be represented as f(x) = x²

Describing the transformation

First, we have a reflection across the y-axis

This gives

f(x) = -x²

Next, we have a vertical compression by 2

So, we have

f(x) = -2x²

Next, we have a translation right by 1 unit

So, we have

f(x) = -2(x - 1)²

Lastly, we have a translation up by 2 units

So, we have

f(x) = -2(x - 1)² + 2

Hence, the transformed function is f(x) = -2(x - 1)² + 2

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