Mathematics
Grade10
Easy
Question
A function f is defined by the rule -0.5x + 1 for the domain x < 1 and by the rule x for the domain x ≥ 1. Write the piecewise-defined function f using function notation
- f(x) : {(-0.5x + 1 , x ≥ 1) , (x , x < 1)}
- f(x) : {(x , x ≥ 1) , (-0.5x , x < 1)}
- f(x) : {(x , x ≥ 1) , (-0.5x + 1 , x < 1)}
- f(x) : {(0.5x , x ≥ 1) , (-0.5x + 1 , x < 1)}
Hint:
We proceed with one step at a time and build the function. Lastly, we combine all the pieces of the function.
The correct answer is: f(x) : {(x , x ≥ 1) , (-0.5x + 1 , x < 1)}
Step 1 of 3:
First, we have the rule -0.5x + 1 for the domain x < 1, viz., (-0.5x + 1, x < 1) ...(*)
Step 2 of 3:
Then, we have the rule x for the domain x ≥ 1, viz., (x, x ≥ 1) ...(**)
Step 3 of 3:
Combining (*) and (**), we get f(x) : {(x, x ≥ 1), (-0.5x + 1, x < 1)}
Final Answer:
The right choice is- c. f(x) : {(x , x ≥ 1) , (-0.5x + 1 , x < 1)}
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