Kenji uses the diagram to determine the quotient of StartFraction 9 Over 10 EndFraction and Three-fifths. A fraction bar labeled 1. Under the 1 are 10 boxes labeled StartFraction 1 Over 10 EndFraction. Under the 10 boxes are 5 boxes labeled one-fifth. He arrives at an answer of 4 and one-half. Which could be Kenji’s error? Kenji counted by One-fifth instead of Three-fifths. Kenji computed the division backwards, Three-fifths divided by StartFraction 9 Over 10 EndFraction. Kenji used the wrong fractional part to represent what was left over. Instead of a number of out 2, the number should be out of 5. Kenji used the wrong fractional part to represent what was left over. Instead of a number of out 2, the number should be out of 10.

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let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

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