Question

a rock is thrown 64 feet into the air off of a 76-foot cliff. the graph shows the height of the rock as a function of time. which inequality represents the range of the function? a. $0 \leq y \leq 64$ b. $0 \leq y \leq 140$ c. $5 \leq y \leq 140$ d. $76 \leq y \leq 140$

Explanation:

Step1: Understand Range of a Function

The range of a function is the set of all possible output values (y - values) it can take. For the graph of the rock's height over time, we look at the minimum and maximum y - values.

Step2: Analyze the Graph's y - values

• The minimum height (y - value) occurs when the rock hits the ground. From the graph, the lowest y - value is 0 (when time x = 5 seconds, height y = 0).
• The maximum height (y - value) from the graph is 140 (the peak of the parabola - shaped graph).

Step3: Evaluate the Options

• Option A: \(0\leq y\leq64\) is incorrect because the maximum height is 140, not 64.
• Option B: \(0\leq y\leq140\) matches our analysis of the minimum (0) and maximum (140) y - values.
• Option C: \(5\leq y\leq140\) is incorrect because the minimum y - value is 0 (when the rock is on the ground), not 5.
• Option D: \(76\leq y\leq140\) is incorrect because the rock starts from a 76 - foot cliff but then falls to the ground (y = 0), so the minimum y - value is 0, not 76.

Answer:

B. \(0\leq y\leq140\)