Question

sketch the graph of the first function. then, on the same coordinate plane, use a transformation to sketch the second graph. y = √(49 - x^2), y = -√(49 - x^2) which graph shows y = √(49 - x^2) in red and y = -√(49 - x^2) in blue? a. b. c. d.

Explanation:

Step1: Analyze the first - function

The function $y = \sqrt{49 - x^{2}}$ can be rewritten as $y^{2}=49 - x^{2}$ or $x^{2}+y^{2}=49(y\geq0)$. It represents the upper - half of the circle centered at the origin $(0,0)$ with radius $r = 7$ (since for a circle equation $(x - a)^{2}+(y - b)^{2}=r^{2}$, here $a = 0$, $b = 0$, $r = 7$ and we take $y\geq0$ due to the square - root).

Step2: Analyze the second - function

The function $y=-\sqrt{49 - x^{2}}$ can be rewritten as $y^{2}=49 - x^{2}$ or $x^{2}+y^{2}=49(y\leq0)$. It represents the lower - half of the circle centered at the origin $(0,0)$ with radius $r = 7$.

Step3: Determine the correct graph

The graph of $y = \sqrt{49 - x^{2}}$ (red) should be the upper - half of the circle and $y=-\sqrt{49 - x^{2}}$ (blue) should be the lower - half of the circle.

Answer:

The graph where the red curve is the upper - half of the circle and the blue curve is the lower - half of the circle centered at the origin with radius 7. Without seeing the actual options in detail, the correct graph will have the red curve above the x - axis and the blue curve below the x - axis for the circle $x^{2}+y^{2}=49$.