Question

1. for circle (x - 2)^2+(y + 3)^2 = 49/64, find the center and radius. 11. does the following set describe a function? if so, give the domain and range. if not, tell why. {(-2,3),(-1,1),(-2,4),(0,7)}

Explanation:

Step1: Recall circle - standard form

The standard form of a circle 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 circle $(x - 2)^2+(y+3)^2=\frac{49}{64}$, comparing with the standard form, we have $h = 2$ and $k=-3$. So the center is $(2,-3)$.

Step3: Calculate the radius

Since $r^2=\frac{49}{64}$, then $r=\sqrt{\frac{49}{64}}=\frac{7}{8}$.

Step4: Analyze the set for function - definition

A set of ordered pairs $(x,y)$ is a function if for each $x$ - value there is exactly one $y$ - value. In the set $\{(-2,3),(-1,1),(-2,4),(0,7)\}$, the $x$ - value $x = - 2$ is paired with two different $y$ - values ($y = 3$ and $y = 4$). So it is not a function.

Answer:

1. Center: $(2,-3)$; Radius: $\frac{7}{8}$
2. It is not a function because the input $x=-2$ has two different outputs ($y = 3$ and $y = 4$).