Question

leon throws a ball off a cliff. the graph represents a relation that models the ball’s height, h, in feet over time, t, in seconds. what is the domain? \\( \circ \\{t|0 \leq t \leq 3\\} \\) \\( \circ \\{t|0 \leq t \leq 48\\} \\) \\( \circ \\{t|0 \leq t \leq 64\\} \\) \\( \circ \\{t| \text{all real numbers}\\}\\)

Explanation:

Step1: Define domain for this problem

The domain here is all valid time values \(t\) (in seconds) for which the ball has a measurable height.

Step2: Identify minimum \(t\) value

The ball is thrown at \(t=0\) (point \((0, 48)\)), so the smallest \(t\) is 0.

Step3: Identify maximum \(t\) value

The ball hits the ground at \(t=3\) (point \((3, 0)\)), so the largest \(t\) is 3.

Step4: State the domain

The domain includes all \(t\) from 0 to 3, inclusive.

Answer:

\(\{t\mid 0 \leq t \leq 3\}\)