Finding Limits

Question 12 • Precalculus

Using the extreme value theorem, which graph has a maximum of 5 and minimum of –3?

Answer

On a coordinate plane, a curve starts at closed circle (negative 1, negative 3) and curves up and approaches the y-axis in quadrant 2. A curve starts at closed circle (2, 5) and curves up and approaches x = 1 in quadrant 1.

On a coordinate plane, a curve starts at closed circle (negative 2, negative 3), curves up to (1, 0.5), curves down through (0, negative 1) to (0.5, negative 1.75), and curves up to closed circle (2, 5).

On a coordinate plane, a line starts at closed circle (negative 3, negative 3) and goes to closed circle (5, 1).

On a coordinate plane, a curve starts at closed circle (negative 4, negative 3), curves up to (1.5, 7.5) and curves down to closed circle (4, 5).

Explanation

Choice B shows a continuous curve on a closed interval, with closed endpoints at y = −3 and y = 5. The curve’s intermediate values stay between those endpoint values, so its minimum is −3 and its maximum is 5. Choice D reaches 7.5, while choice C never reaches 5.

AI-written and checked against the verified answer.

More from this Course

Recursive Formulas

Dot Product and Work

Arithmetic Series