Question

graph the equation shown below by transforming the given graph of the parent function.
$y = \sqrt{x} + 4$
answer attempt 2 out of 2
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Explanation:

Step1: Identify parent function

Parent function is $y=\sqrt{x}$ (graphed).

Step2: Define vertical shift rule

For $y=f(x)+k$, shift up by $k$ units.
Here $k=4$, so shift $y=\sqrt{x}$ up 4.

Step3: Transform key points

• Parent point $(0,0)$: $(0, 0+4)=(0,4)$
• Parent point $(1,1)$: $(1, 1+4)=(1,5)$
• Parent point $(4,2)$: $(4, 2+4)=(4,6)$
• Parent point $(9,3)$: $(9, 3+4)=(9,7)$

Step4: Plot and connect points

Draw a curve through $(0,4)$, $(1,5)$, $(4,6)$, $(9,7)$.

Answer:

The graph of $y=\sqrt{x}+4$ is the parent square root function shifted vertically upward by 4 units, passing through the points $(0,4)$, $(1,5)$, $(4,6)$, and $(9,7)$.