g(0)=
Ask yourself: What is x?
Answer: It's 0, because in g(0), 0 replaces x in g(x).
Ask yourself: What is the value of x?
Answer: It's 0.
Ask yourself: Which one of these, x < -5 or x > -5, does 0 fall
under?
Answer: 0 falls in x > -5 because 0 is greater than any negative
number.
Ask yourself: What expression does the piece-wise function above, g(x),
say to use if x > -5?
Answer: It says to use x+5 if x > -5.
Ask yourself: So what do I do?
Answer: You do exactly what it says to do, use x+5.
Ask yourself: How do I use x+5?
Answer: You substitute 0 for x in x+5, getting 0+5, or 5.
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g(-7)=
Ask yourself: What is x?
Answer: It's -7, because in g(-7), -7 replaces x in g(x).
Ask yourself: What is the value of x?
Answer: It's -7.
Ask yourself: Which one of these, x < -5 or x > -5, does -7 fall
under?
Answer: -7 falls in x < -5 because -7 is further to the left on the number
line than -5.
Ask yourself: What expression does the piece-wise function above, g(x),
say to use if x < -5?
Answer: It says to use -(x+5) if x > -5.
Ask yourself: So what do I do?
Answer: You do exactly what it says to do, use -(x+5).
Ask yourself: How do I use -(x+5)?
Answer: You substitute -7 for x in -(x+5), getting -(-7+5), or -(-2) or 2.
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g(2)=
Ask yourself: What is x?
Answer: It's 2, because in g(2), 2 replaces x in g(x).
Ask yourself: What is the value of x?
Answer: It's 2.
Ask yourself: Which one of these, x < -5 or x > -5, does 2 fall
under?
Answer: 2 falls in x > -5 because any positive number is greater than
any negative number.
Ask yourself: What expression does the piece-wise function above, g(x),
say to use if >?
Answer: It says to use x+5 if x > -5.
Ask yourself: So what do I do?
Answer: You do exactly what it says to do, use x+5.
Ask yourself: How do I use x+5?
Answer: You substitute 2 for x in x+5, getting 2+5, or 7.
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Edwin