sketch the graph of the function, not by plotting points, but by starting with the graph of a standard…

sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations.\n$f(x)=(x + 3)^{2}$

sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations.\n$f(x)=(x + 3)^{2}$

Answer

Explanation:

Step1: Identify the standard function

The standard function is (y = x^{2}), which is a parabola with vertex at ((0,0)) and opens upwards.

Step2: Analyze the transformation

For the function (f(x)=(x + 3)^{2}), we use the transformation rule (y = f(x + h)) which shifts the graph of (y = f(x)) horizontally. If (h>0), the graph shifts to the left by (h) units. Here (h = 3), so the graph of (y=x^{2}) shifts to the left by (3) units.

The vertex of (y=(x + 3)^{2}) is at ((- 3,0))

Answer:

The third option (the parabola with vertex at ((-3,0))) is the correct graph.