Mathematics
Grade10
Easy

Question

Compare the graph of h open parentheses x close parentheses equals 4 to the power of x minus 3 end exponent plus 5 to the graph of h open parentheses x close parentheses equals 4 to the power of x end exponent.

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

Hint:

we know that g open parentheses x close parentheses equals a to the power of x minus h end exponent is the horizontal translation of f open parentheses x close parentheses equals a to the power of x end exponent by h units. If h is greater than 0 the graph will move right and if h is less than 0 the graph will move left. f(x)=a to the power of x+k is the vertical translation of the graph f(x)=a to the power of x, where the graph moves upward by k units.

The correct answer is: 3 units to the right and 5 units up


    The graph of f left parenthesis x right parenthesis equals a to the power of x minus h end exponent is a horizontal translation of the graph of f left parenthesis x right parenthesis equals a to the power of x end exponent. If h is greater than 0 the graph will move right.
    The graph of f left parenthesis x right parenthesis equals a to the power of x end exponent plus k is a vertical translation of the graph of f left parenthesis x right parenthesis equals a to the power of x end exponent. The graph will move upward.
    In h open parentheses x close parentheses equals 4 to the power of x minus 3 end exponent plus 5, the graph of the parent function is translated both horizontally and vertically.
    It is translated 3 units to the right and 5 units up.

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