Question

week 6 homework
practice score: 11.08/22 answered: 15/22
question 17
the graph above is a transformation of the function f(x)=|x|.
write an equation for the function graphed above.
g(x)=
question help: video 1 video 2

Explanation:

Step1: Analyze vertical shift

The vertex of \(y = |x|\) is at \((0,0)\), and the vertex of the given graph is at \((2,1)\). There is a vertical shift of 1 unit up. So we start with \(y=|x|+ 1\).

Step2: Analyze horizontal shift

The vertex has also shifted 2 units to the right. For a horizontal shift \(h\) of the absolute - value function \(y = |x|\), the general form is \(y=|x - h|\). Here \(h = 2\), so the function becomes \(g(x)=|x - 2|+1\).

Answer:

\(g(x)=|x - 2|+1\)