Question

question
the graph of ( y = 3f(x - 2)+4 ) is the graph of ( y = f(x) )
select the correct answer below:
vertically stretched by a factor of 3, shifted right 2 units and up 4 units
vertically compressed by a factor of 3, shifted right 2 units and up 4 units
vertically stretched by a factor of 3, shifted left 2 units and up 4 units
vertically compressed by a factor of 3, shifted left 2 units and up 4 units

Explanation:

Step1: Analyze vertical transformation

For the function \(y = af(x - h)+k\), when \(|a|> 1\), it is a vertical stretch. Here \(a = 3>1\), so it is a vertical stretch by a factor of 3.

Step2: Analyze horizontal transformation

For the function \(y = f(x - h)\), when \(h>0\), the graph shifts to the right. Here \(h = 2>0\), so it shifts right 2 units.

Step3: Analyze vertical shift

For the function \(y = f(x)+k\), when \(k>0\), the graph shifts up. Here \(k = 4>0\), so it shifts up 4 units.

Answer:

vertically stretched by a factor of 3, shifted right 2 units and up 4 units