Question

use transformations to graph the function.
$m(x)=3\sqrt{x + 2}-3$

Explanation:

Step1: Identify parent function

Parent function: $f(x)=\sqrt{x}$

Step2: Apply horizontal shift

Shift left 2 units: $f(x+2)=\sqrt{x+2}$

Step3: Apply vertical stretch

Stretch by factor 3: $3f(x+2)=3\sqrt{x+2}$

Step4: Apply vertical shift

Shift down 3 units: $3\sqrt{x+2}-3$

Step5: Plot key points

• Parent $f(x)$ key points: $(0,0), (1,1), (4,2), (9,3)$
• Transformed points:

$(0-2, 3*0-3)=(-2,-3)$
$(1-2, 3*1-3)=(-1,0)$
$(4-2, 3*2-3)=(2,3)$
$(9-2, 3*3-3)=(7,6)$

Answer:

The graph of $m(x)=3\sqrt{x+2}-3$ is the parent square root function shifted left 2 units, vertically stretched by a factor of 3, and shifted down 3 units. Key points to plot are $(-2,-3)$, $(-1,0)$, $(2,3)$, and $(7,6)$, connected by a curve starting at $(-2,-3)$ and increasing slowly.