describe the transformation $f(x)=sqrt{x + 1}-5$ in words. the parent function $f(x)=sqrt{x}$ has been…
describe the transformation $f(x)=sqrt{x + 1}-5$ in words. the parent function $f(x)=sqrt{x}$ has been shifted 1 unit and 5 units.
Answer
Explanation:
Step1: Analyze horizontal shift
For a function $y = f(x + h)$, if $h>0$, the graph shifts left. In $y=\sqrt{x + 1}-5$, compared to $y = \sqrt{x}$, $h = 1$, so it shifts left 1 unit.
Step2: Analyze vertical shift
For a function $y=f(x)+k$, if $k<0$, the graph shifts down. In $y=\sqrt{x + 1}-5$, $k=- 5$, so it shifts down 5 units.
Answer:
left; down