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