On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most circle goes from (negative 3, 3) to (negative 2, 3). Each segment is one unit lower and 1 unit farther to the right than the previous segment. The right-most segment is just a closed circle at (3, negative 3).
Which function and domain could represent the given graph?
f(x) = 1 – ⌊x⌋; –3 < x < 3
f(x) = 1 + ⌊x⌋; –3 ≤ x ≤ 3
f(x) = –⌊x⌋; –3 ≤ x ≤ 3
f(x) = ⌊x⌋; –3 < x < 3
Answers
On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle
Concept:
The step function is also known as floor. It gives a line segment with dark and open end points according to their values.
It always takes integer values not any fractional value, that's why it given strips on y-axis
Given:
A horizontal segments that are each 1 unit long
The left end of each segment is a closed circle
The right end of each segment is an open circle
The starting of the segments is -3 and takes values 3 on y-axis
The end of the segment is at x = 3 and the y-axis value at x= 3 is -3
Find:
The function and domain of that graph
Solution:
Since start from -3 with left dark circle and right open circle with getting value 2 that means the floor (x) is negative.
Since -floor (x) never attains 2 in its range therefore the function only be 1- floor (x)
The domain will be -3≤x≤3
Hence the correct option is (1).
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