The graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉ as the graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.
Modulus function / Absolute function [x]
What is modulus function?
A modulus function is a function that determines a number or variable's absolute value. No matter what input was provided to this function, the outcome is always positive.
Solution of function f(x) = [x]
Consider different values for x.
Say,
x = -1; f(-1) = [-1] = 1
x = 1; f(1) = [1] = 1
For any value of the x, the value of the function will be positive only.
The graph is attached in the image.
Solution of function f(x) = [x] + 7
Consider different values for x.
Say,
x = 0; f(0) = [0] + 7 = 0 + 7; f(0) = 7
x = -1; f(-1) = [-1] + 7 = 1 + 7; f(-1) = 8
x = 1; f(1) = [1] = 1 + 7; f(1) = 8
For any value of the x, the value of the function will be positive only, but it would be 7 units shifted up on the y axis.
The graph is attached in the image.
To know more about how to determine modulus of complex numbers?, here
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