Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range. (x + 1)^2 + y^2 = 16

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.

Step2: Identify the center

For the equation $(x + 1)^2+y^2 = 16$, we can rewrite it as $(x-(-1))^2+(y - 0)^2=4^2$. So the center $(h,k)=(-1,0)$.

Step3: Identify the radius

Since $r^2 = 16$, then $r = 4$.

Step4: Find the domain

The left - most $x$ value is $h-r=-1 - 4=-5$ and the right - most $x$ value is $h + r=-1+4 = 3$. So the domain is $[-5,3]$.

Step5: Find the range

The bottom - most $y$ value is $k - r=0 - 4=-4$ and the top - most $y$ value is $k + r=0 + 4=4$. So the range is $[-4,4]$.

Answer:

Center: $(-1,0)$; Radius: $4$; Domain: $[-5,3]$; Range: $[-4,4]$