All non-vertical lines are functions, since for any 'x' value, only one 'y' value can exist. Note the largest exponent on 'y' is 1, giving a maximum of 1 answer for 'y' for every 'x' value.

All non-vertical lines pass the vertical line test.

Question 1

Determine whether or not  y=4x-7  is a function.

 

yes

no

not today

All vertical lines are relations only, since for any 'x' value, many  'y' values can exist.

All vertical lines fail the vertical line test.

 

Determine whether or not  x=3  is a function.

  

yes

no

no 'y' value exist, so no points exist

.

Since for any 'x' value, only one 'y' value can exist, this is a function.  Note the largest exponent on 'y' is 1, giving a maximum of 1 answer for 'y' for every 'x' value.

Question 3

Determine whether or not  y = x² - 4x  is a function.

 

yes

no

this is not a line

Although the dependent variable, and the equation are not in the usual position, for each 'x' value, two  'y' values can exist. Note the largest exponent on 'y' is 2, giving a maximum of 2 answers for 'y' given any 'x' value.

Determine whether or not  x = y² - 4y   is a function.

 

yes

no

please ask someone else

All regions are relations, since for any 'x' value, many 'y' value can exist.

Question 5

Determine whether or not  y < 4x - 3  is a function.

 

yes

no

this is not a line

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