Question

josh is exploring the formula for the circumference of a circle. he computed the circumferences of several circles with different radii. he then plotted the results and connected them with a line, as shown below. the graph shows the circumference (in cm) versus the radius (in cm). find the domain and the range of the function shown. write your answers as inequalities, using x or y as appropriate. or, you may instead click on \empty set\ or \all reals\ as the answer. (a) domain: (b) range: try again

Explanation:

Step1: Identify the domain variable

The domain is related to the radius. Radius cannot be negative in the context of circles.

Step2: Determine the domain inequality

The smallest value of the radius shown on the graph is a non - zero positive value. So the domain is \(x>0\).

Step3: Identify the range variable

The range is related to the circumference. Since the circumference is calculated based on a positive radius and the formula \(C = 2\pi r\) (\(r>0\)), the circumference is also positive.

Step4: Determine the range inequality

The smallest value of the circumference is also positive. So the range is \(y>0\).

Answer:

(a) domain: \(x > 0\)
(b) range: \(y > 0\)