Question

1. graph the function $f(x) = 3 + \sqrt{x}$.

Explanation:

Step1: Identify parent function

The parent function is $g(x) = \sqrt{x}$, defined for $x \geq 0$, with points like $(0,0)$, $(1,1)$, $(4,2)$, $(9,3)$.

Step2: Determine transformation

$f(x) = 3 + \sqrt{x}$ is a vertical shift up by 3 units of $g(x)$.

Step3: Calculate key points

Add 3 to each $y$-value of $g(x)$:

• For $x=0$: $f(0) = 3 + \sqrt{0} = 3$ → $(0, 3)$
• For $x=1$: $f(1) = 3 + \sqrt{1} = 4$ → $(1, 4)$
• For $x=4$: $f(4) = 3 + \sqrt{4} = 5$ → $(4, 5)$
• For $x=9$: $f(9) = 3 + \sqrt{9} = 6$ → $(9, 6)$

Step4: Plot and connect points

Plot the calculated points on the grid, then draw a smooth curve starting at $(0,3)$ and increasing slowly as $x$ increases.

Answer:

The graph is a vertical shift up 3 units of the square root parent function, passing through points $(0, 3)$, $(1, 4)$, $(4, 5)$, $(9, 6)$, with a domain of $x \geq 0$ and range of $y \geq 3$.