Questions: Graphing a square root function: Problem type 1 Graph the function. f(x) = sqrt(x+2) Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.

Solution Steps

The given function is $f(x) = 1\sqrt{x + 2} + 0$, where:

• $a = 1$ scales the function vertically.
• $b = 1$ affects the horizontal scaling and direction.
• $c = 2$ shifts the graph horizontally.
• $d = 0$ shifts the graph vertically.

The domain of the function is determined by $bx + c \geq 0$. Solving for $x$, we get: $x \geq -2$ for $b > 0$ and $x \leq -2$ for $b < 0$. Thus, the domain is $[-2, \infty)$.

Selected points for plotting are: ($x = -2$, $y = 0$) ($x = 0$, $y = 1.41$) ($x = -1$, $y = 1$) ($x = 0$, $y = 1.41$)

The graph is plotted based on the identified points. The characteristic curve of the square root function is adjusted according to the transformations specified by $a$, $b$, $c$, and $d$.

The graph undergoes the following transformations:

• Vertical scaling by a factor of $a = 1$.
• Horizontal scaling and reflection (if $b < 0$) by a factor of $b = 1$.
• Horizontal shift by $c = 2$ (to the left if $c > 0$, to the right if $c < 0$).
• Vertical shift by $d = 0$ (upwards if $d > 0$, downwards if $d < 0$).

Final Answer: