Relations and Functions: common misconceptions

If your child says… “Changing the order makes no difference.”

Ask together

Would swapping 1 and 3 keep their point in the same position?

What’s true

Switching different entries changes an ordered pair.

If your child says… “The counts match, so the products match.”

Ask together

Can the reversed product start a pair with 0?

What’s true

Reversed products coincide only when their factors match or either factor is empty.

If your child says… “Only the first inside set needs A.”

Ask together

Where would the first entry of the second pair come from without A?

What’s true

Both resulting products need the outside factor.

If your child says… “The range includes everything in B.”

Ask together

Which arrow reaches 0?

What’s true

The range includes reached targets, while the codomain includes every allowed target.

If your child says… “Different inputs need different outputs.”

Ask together

Does a gain another output just because b reaches the same place?

What’s true

A function permits shared outputs but requires exactly one output for every input.

If your child says… “I can ignore the input’s negative sign.”

Ask together

What number multiplied by negative one gives positive one?

What’s true

Substitution keeps the input’s sign.

If your child says… “A negative input stays negative inside the bars.”

Ask together

Can a distance below zero describe how far apart two points are?

What’s true

Modulus measures distance from zero, so its output cannot be negative.

If your child says… “The minus changes only the first term.”

Ask together

Have you subtracted the whole second output if you add its one?

What’s true

Subtracting a bracket subtracts every term inside.