The set of all x-intercepts of $f ( x ) = \lceil x \rceil - 1$ is

A) $( 0,1 ]$
B) $[ 0,1 )$
C) $[ 1,2 )$
D) $(1,2)$
E) $( 1,2 ]$

Name: The set of all x-intercepts of $f ( x ) = \lceil x \rceil - 1$ is A) $( 0,1 ]$ B) $[ 0,1 )$ C) $[ 1,2 )$ D) $(1,2)$ E) $( 1,2 ]$
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Question

The set of all x-intercepts of $f ( x ) = \lceil x \rceil - 1$ is

A) $( 0,1 ]$
B) $[ 0,1 )$
C) $[ 1,2 )$
D) $(1,2)$
E) $( 1,2 ]$

Quizplus · Accepted Answer

The x-intercept occurs when $f(x) = 0$, so $\lceil x \rceil - 1 = 0$ implies $\lceil x \rceil = 1$. This is true for $0 < x \leq 1$, which corresponds to the interval $(0, 1]$.

The Set of All X-Intercepts Of f(x)=⌈x⌉−1f ( x ) = \lceil x \rceil - 1f(x)=⌈x⌉−1

The Set of All X-Intercepts Of $f ( x ) = \lceil x \rceil - 1$