Question
Express the function as a piecewise-defined function.
f(x) = 0.5 IxI
- f(x) : {(0.5x , x ≥ 0) , (-0.5x , x < 0)}
- f(x) : {(5x , x ≥ 0) , (-5x , x < 0)}
- f(x) : {(0.5x , x < 0) , (-0.5x , x > 0)}
- f(x) : {(5x , x ≤ 0) , (-5x , x > 0)}
Hint:
A piecewise-defined function is one that is defined not by a single equation, but by two or more. Each equation is valid for some interval.
We simply check the values of f(x) for different values of x and find out the corresponding piecewise-defined function f using function notation.
The correct answer is: f(x) : {(0.5x , x ≥ 0) , (-0.5x , x < 0)}
Step 1 of 1:
Given, f(x) = 0.5 IxI
x = -2 , f(x) = 1
x = -1 , f(x) = 0.5
x = 0 , f(x) = 0
x = 1, f(x) = 0.5
x = 2, f(x) = 1
Hence, we have f(x): {(0.5x, x≥0), (-0.5x, x<0)}
Final Answer:
The right choice is- b. f(x) : {(0.5x , x ≥ 0) , (-0.5x , x < 0)}
Related Questions to study
Evaluate the following piecewise function for x = 0 and x = 5
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Evaluate the following piecewise function for x = 0 and x = 5
f(x) = 2x - 3 , x < 0
f(x) = x² - 1 , x = 0
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