Limits and Continuity — Quiz

Question 10 • Precalculus

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

Answer

Image with description 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).

Image with description 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.

Image with description 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).

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

Explanation

The Extreme Value Theorem applies to a continuous curve on a closed interval, so its maximum and minimum are attained. In graph A, the curve is continuous and has closed endpoints at y = −3 and y = 5; its values in between stay within those bounds. Therefore, its minimum is −3 and its maximum is 5.

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