consider the following function. f(x)=-2√x + 5 step 1 of 2: graph the original function by indicating how…

consider the following function. f(x)=-2√x + 5 step 1 of 2: graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.

consider the following function. f(x)=-2√x + 5 step 1 of 2: graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.

Answer

Explanation:

Step1: Identify the basic function

The basic function is $y = \sqrt{x}$.

Step2: Analyze the coefficient of $\sqrt{x}$

The coefficient -2 reflects the graph of $y=\sqrt{x}$ about the $x$-axis and vertically stretches it by a factor of 2.

Step3: Analyze the constant term

The + 5 shifts the graph of $y=-2\sqrt{x}$ up 5 units.

To graph:

  1. First, consider the domain of $f(x)=-2\sqrt{x}+5$. Since the square - root function requires $x\geq0$, the domain is $[0,\infty)$.
  2. The basic points of $y = \sqrt{x}$ are $(0,0),(1,1),(4,2)$.
  3. For $y=-2\sqrt{x}$, the points become $(0,0),(1, - 2),(4,-4)$ after reflection and stretching.
  4. For $y=-2\sqrt{x}+5$, the points become $(0,5),(1,3),(4,1)$. Plot these points and draw a smooth curve starting from $(0,5)$ and extending to the right.

Answer:

Graph the function by first reflecting and stretching $y = \sqrt{x}$ about the $x$-axis and vertically by a factor of 2, then shifting up 5 units. Plot points $(0,5),(1,3),(4,1)$ and draw a smooth curve for $x\geq0$.