Mathematics
Functions
Easy

Question

Study the graph and choose the correct option.

  1. The graph is decreasing in intervals (1) and (4)
  2. The graph shows a constant function in interval (2)  
  3. The graph is increasing in intervals (2) and (4)
  4. The graph has a constant rate of change

The correct answer is: The graph is decreasing in intervals (1) and (4)

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If the table represents the function, then the charges for parking at zoo for 6 hrs is
Time (up to hrs.)
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text  If  end text f colon R not stretchy rightwards arrow R comma f left parenthesis x right parenthesis equals x cubed plus 3 comma text  and  end text g colon R not stretchy rightwards arrow R comma g left parenthesis x right parenthesis equals 2 x plus 1 text  then  end text f to the power of negative 1 end exponent o g to the power of negative 1 end exponent left parenthesis 23 right parenthesis text  equals  end text

text  If  end text f colon R not stretchy rightwards arrow R comma f left parenthesis x right parenthesis equals x cubed plus 3 comma text  and  end text g colon R not stretchy rightwards arrow R comma g left parenthesis x right parenthesis equals 2 x plus 1 text  then  end text f to the power of negative 1 end exponent o g to the power of negative 1 end exponent left parenthesis 23 right parenthesis text  equals  end text

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text  Let  end text f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction text  then  end text f left square bracket f left parenthesis x right parenthesis right square bracket equals x text  provided that  end text

text  Let  end text f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction text  then  end text f left square bracket f left parenthesis x right parenthesis right square bracket equals x text  provided that  end text

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text  If the function  end text f colon R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow A text  defined by  end text f left parenthesis x right parenthesis equals fraction numerator x squared over denominator 1 minus x squared end fraction comma text end textis surjective then A =

text  If the function  end text f colon R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow A text  defined by  end text f left parenthesis x right parenthesis equals fraction numerator x squared over denominator 1 minus x squared end fraction comma text end textis surjective then A =

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text  If  end text f colon R not stretchy rightwards arrow A text  defined by  end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction straight for all x element of R text  is surjective, then  end text A equals

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