Question

sec 3.5 transformation of functions: problem 5 (1 point) describe how the graph of $g(x)=|x - 9|-10$ can be obtained from $f(x)=|x|$. the graph of $g(x)$ is the graph of $f(x)$: shifted select units and shifted select units. note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Analyze horizontal shift

For a function $y = f(x - h)$, the graph of $y = f(x)$ is shifted $h$ units to the right. In $g(x)=|x - 9|-10$, comparing with $f(x)=|x|$, we have $h = 9$. So the graph is shifted 9 units to the right.

Step2: Analyze vertical shift

For a function $y=f(x)+k$, the graph of $y = f(x)$ is shifted $k$ units up if $k>0$ and $|k|$ units down if $k < 0$. In $g(x)=|x - 9|-10$, we have $k=- 10$. So the graph is shifted 10 units down.

Answer:

shifted 9 units to the right and shifted 10 units down.