AnswersAlgebra IStep Functions — QuizQuestion 6
6
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Step Functions — Quiz

Question 6 • Algebra I

Which is the graph of the step function f of x ? f of x is equal to negative 1 when x is less than negative 1; f of x is equal to 0 when negative 1 is less than or equal to x comma x is less than or equal to 1; f of x is equal to 1 when x is greater than 1

Answer
A
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).
B
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).
C
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to the right at y = 1.
D
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line has a closed circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has a closed circle at (1, 1) and continues horizontally to the right at y = 1.

Explanation

For x < -1, the graph is at y = -1 and has an open circle at (-1, -1), since x = -1 is not included in that interval. From x = -1 through x = 1, the graph is at y = 0 with closed circles at both endpoints. For x > 1, it is at y = 1 with an open circle at (1, 1). These endpoint markings and directions match choice C.

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