Question

1. a cylinder contains 30 milliliters of water. the water begins to leak out as represented by the linear function graphed below. identify the intercepts and interpret what they mean in this situation.

volume of water in cylinder

a. (0,30) and (6,0) the cylinder is empty after 30 seconds and it starts with 6 ml of water
b. (0,30) and (6,0) the cylinder is empty after 6 seconds and it starts with 30 ml of water
c. (30,0) and (0,6) the cylinder is empty after 30 seconds and it starts with 6 ml of water
d. (30,0) and (0,6) the cylinder is empty after 6 seconds and it starts with 30 ml of water

1. which statement about this function is not true?

a. its domain is -4,6
b. its range is -1,4
c. its y-intercept is at (0,2)
d. it has a maximum value of 6

Explanation:

Question 5

Step1: Analyze the graph's axes

The x - axis represents time (in seconds) and the y - axis represents volume (in milliliters). At \(x = 0\) (time = 0), the volume \(y=30\) mL (so the point is \((0,30)\)). At \(y = 0\) (volume = 0), the time \(x = 6\) seconds (so the point is \((6,0)\)).

Step2: Interpret the intercepts

The y - intercept \((0,30)\) means at time \(t = 0\) (start), the volume of water is 30 mL. The x - intercept \((6,0)\) means at time \(t=6\) seconds, the volume of water is 0 mL (the cylinder is empty). Now let's check the options:

• Option a: Interprets the intercepts wrong (swaps the meanings of the intercepts).
• Option b: Correctly identifies the intercepts \((0,30)\) and \((6,0)\) and their meanings.
• Option c: Wrong intercepts and wrong interpretations.
• Option d: Wrong intercepts.

Step1: Analyze the domain

The domain of a function is the set of all x - values. From the graph, the leftmost point has \(x=- 4\) and the rightmost point has \(x = 6\), so the domain is \([-4,6]\), so option a is true.

Step2: Analyze the range

The range is the set of all y - values. The lowest y - value is \(-1\) and the highest y - value is 4, so the range is \([-1,4]\), so option b is true.

Step3: Analyze the y - intercept

The y - intercept is the point where \(x = 0\). From the graph, when \(x = 0\), \(y=2\), so the y - intercept is \((0,2)\), so option c is true.

Step4: Analyze the maximum value

The maximum y - value on the graph is 4 (not 6), so the statement "It has a maximum value of 6" is false.

Answer:

b. \((0,30)\) and \((6,0)\) the cylinder is empty after 6 seconds and it starts with 30 mL of water

Question 6