Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range.
x² + y² = 49
use the graphing tool to graph the equation.
click to enlarge graph
what is the domain?
the domain is . (type your answer in interval notation.)
what is the range?
the range is . (type your answer in interval notation.)

Explanation:

Step1: Recall circle - equation form

The standard form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. For the equation $x^{2}+y^{2}=49$, we can rewrite it as $(x - 0)^2+(y - 0)^2 = 7^2$.

Step2: Determine center and radius

Comparing with the standard - form, the center $(h,k)=(0,0)$ and the radius $r = 7$.

Step3: Find the domain

The left - most and right - most points of the circle are found by considering the $x$ - values. Since the radius is 7, the $x$ - values range from $-7$ to 7. In interval notation, the domain is $[-7,7]$.

Step4: Find the range

The bottom - most and top - most points of the circle are found by considering the $y$ - values. Since the radius is 7, the $y$ - values range from $-7$ to 7. In interval notation, the range is $[-7,7]$.

Answer:

Center: $(0,0)$
Radius: $7$
Domain: $[-7,7]$
Range: $[-7,7]$