Understanding the Concept of a Limit — Quiz

Question 6 • Precalculus

Which graph of f of x satisfies these conditions? limit x to 2 raised to the negative power of f times x is equal to negative 4 and limit x to 2 raised to the plus power of f times x is equal to 0

Answer

Image with description On a coordinate plane, a line starts at closed circle (2, negative 4) and goes up through (negative 2, 0). A curve starts at open circle (2, 0) and goes to open circle (4, 2). A line starts at closed circle (4, negative 2) and goes to (6, negative 2).

Image with description On a coordinate plane, a line starts at closed circle (0, negative 3), goes to closed circle (negative 2, negative 4), and then goes to (negative 6, 4). A curve starts at open circle (0, 2) and curves down to open circle (2, 0). A line starts at closed circle (2, negative 2) and goes down to (6, negative 6).

Image with description On a coordinate plane, a line starts at closed circle (2, negative 2), goes to closed circle (negative 2, negative 4), and then goes to (negative 6, 4). A curve starts at open circle (2, 0) and curves to open circle (4, 2). A line starts at closed circle (4, negative 2) and goes to (6, negative 2).

Image with description On a coordinate plane, a line starts at closed circle (0, negative 2) and goes to (negative 6, negative 2). A curve starts at open circle (0, 2) and curves down to open circle (2, 0). A line starts at closed circle (2, negative 4) and goes to (6, 0).

Explanation

As x approaches 2 from the left, the graph must approach y = -4. As x approaches 2 from the right, it must approach y = 0. Choice A shows the left-hand piece approaching (2, -4) and the right-hand piece approaching the open circle at (2, 0), so it satisfies both limits.

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