Mathematics
Grade10
Easy

Question

Compare the graph of h open parentheses x close parentheses equals 2 to the power of x plus 5 end exponent minus 7 to the graph of h open parentheses x close parentheses equals 2 to the power of x end exponent.

  1. 7 units up and 5 units to the right    
  2. 12 units to the right    
  3. 5 units to the left and 7 units down    
  4. 2 units left    

Hint:

We know that the graph of f left parenthesis x right parenthesis equals 2 to the power of x plus h end exponent is a horizontal translation by h units to the left of the graph of f left parenthesis x right parenthesis equals 2 to the power of x end exponent. The graph of f left parenthesis x right parenthesis equals 2 to the power of x minus k is a vertical translation by k unit downwards of the graph of f left parenthesis x right parenthesis equals 2 to the power of x end exponentIn h open parentheses x close parentheses equals 2 to the power of x plus 5 end exponent minus 7, the graph of the parent function is translated both horizontally and vertically.

The correct answer is: 5 units to the left and 7 units down


    The graph of f left parenthesis x right parenthesis equals 2 to the power of x plus h end exponent is a horizontal translation by h units to the left of the graph of f left parenthesis x right parenthesis equals 2 to the power of x end exponent
    The graph of f left parenthesis x right parenthesis equals 2 to the power of x minus k is a vertical translation by k unit downwards of the graph of f left parenthesis x right parenthesis equals 2 to the power of x end exponent.
    In h open parentheses x close parentheses equals 2 to the power of x plus 5 end exponent minus 7, the graph of the parent function is translated both horizontally and vertically.
    It is translated 5 units to the left and 7 units down.

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