Question

score on last try: 0 of 1 pt. see details for more.
next question get a similar question you can retry this question belo
given the graph of $f(x)=\sqrt{x}$ graph $g(x)=\sqrt{x}+1$
question help: video

Explanation:

Step1: Identify vertical shift rule

For $g(x)=f(x)+k$, shift $f(x)$ up by $k$.
Here, $g(x)=\sqrt{x}+1=f(x)+1$, so $k=1$.

Step2: Find key points of $f(x)$

Key points of $f(x)=\sqrt{x}$:

• When $x=0$, $f(0)=\sqrt{0}=0$ → $(0,0)$
• When $x=1$, $f(1)=\sqrt{1}=1$ → $(1,1)$
• When $x=4$, $f(4)=\sqrt{4}=2$ → $(4,2)$

Step3: Shift points up by 1 unit

Add 1 to each $y$-coordinate:

• $(0,0+1)=(0,1)$
• $(1,1+1)=(1,2)$
• $(4,2+1)=(4,3)$

Step4: Plot and connect points

Draw a curve through $(0,1)$, $(1,2)$, $(4,3)$, matching the shape of $f(x)$.

Answer:

The graph of $g(x)=\sqrt{x}+1$ is the graph of $f(x)=\sqrt{x}$ shifted vertically upward by 1 unit, passing through the points $(0,1)$, $(1,2)$, and $(4,3)$.