Question

Write the equation for the transformation of f(x) = |x| as shown in the graph.

Answer 1

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

Explanation:

Reason why it's not +3 is because it's the reverse when graphed. But that only applies for the numbers in the brackets. If it's in the brackets and it's positive, you go to the left. If it's negative, then it goes to the right. And as you see, the V isn't on the point (0 , 3), and is in fact, above it, by 1. The graph has also been stretched vertically by 3, it looks like. Hope that was helpful for you!

Answer 2

y = 2|x-3| + 1

Explanation:

The vertex of g(x) = |x| is at (0,0)

We have moved the vertex to ( 3,1)

y = f(x) + C C > 0 moves it up

y = |x| + 1 for the shift up 1

y = f(x + C) C < 0 moves it right

y = |x-3| for the shift to the right 3

y = Cf(x) C > 1 stretches it in the y-direction

y = 2|x| since it is stretched by a factor of 2 in the y direction

Combining

y =2|x-3| + 1