High School Pre-Cal

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What are the domain and range of the piece-wise function below?

             -2 if x<-1

f(x)=∑  x^2 if -1≤ x <1

             -2 if x ≥ 1


A. Domain: all real numbers
Range: all real numbers
B. Domain: all real numbers
Range: [–2,1)
C. Domain: [–2,1)
Range: all real numbers
D. Domain: [–2,1)
Range: [–2,1)

Answer 1

Hi Ken,

 

The domain for this funtion is all real numbers. There are no limitation on x. You could pick any value you want for x to plug into the function.

 

For the range, look at what f(x) can be equal to. 

 

from -∞ up to -1, f(x) = -2

 

from 1 to ∞, f(x) = -2

 

then there's a new definition for f(x) that will approach 1 (as x approaches -1 from the right  and 1 from the left)

 

so it's miniumum is at -2 and it approaches 1 in the other part of the function

 

I wish I could draw this for you to make more sense of it

 

the answer is B

 

f(x) does have a miniumum at -2 : that's why there is a bracket at the beginning of the interval

 

f(x) approaches 1 : that's why there is a parenthesis at the end of the interval