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Subject Test Math 1

Question 13 of 32

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SAT Subject Test

The function f,where f left parenthesis x right parenthesis invisible times equals left parenthesis 1 invisible times plus x right parenthesis to the power of 2 end exponent, is defined for negative 2 invisible times less or equal than x invisible times less or equal than 2. What is the range of f?

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0 invisible times less or equal than text   end text f left parenthesis x right parenthesis invisible times less or equal than text   end text 4

Correct Answer: 
No

0 invisible times less or equal than text   end text f left parenthesis x right parenthesis invisible times less or equal than text   end text 9

Correct Answer: 
Yes

1 less or equal than text   end text f left parenthesis x right parenthesis invisible times less or equal than text   end text 4

Correct Answer: 
No

1 less or equal than text   end text f left parenthesis x right parenthesis invisible times less or equal than text   end text 5

Correct Answer: 
No

1 less or equal than text   end text f left parenthesis x right parenthesis invisible times less or equal than text   end text 9

Correct Answer: 
No

Since left parenthesis 1 invisible times plus x right parenthesis to the power of 2 end exponent is a perfect square, the minimum value of the function is 0, which occurs when x invisible times equals negative 1. The maximum value of f occurs when x invisible times equals 2; f left parenthesis 2 right parenthesis invisible times equals 9. Thus, the range is 0 invisible times less or equal than f left parenthesis x right parenthesis invisible times less or equal than 9. You can also graph the function and see what values the function takes on for the given domain. The graph is a parabola that opens up and has a vertex at left parenthesis negative 1 comma 0 right parenthesis. The correct answer is (B).

Question Difficulty: 
medium