Parent Functions

Parent functions are functions that are altered to form new functions.
Or one can say new functions are altered (transformed) parent functions.
For example y = x (or you may write it f(x) = x) is a parent function and y = x + 2 is a new function based on the parent function.
How do they differ?   answer


Linear function
f(x) = x

   Linear functions are ones whose graph is a straight line and the largest exponent is one.





Quadratic Function
f(x) = x2

Quadratic functions are functions with graphs similar to the one too the left.

The largest exponent is two which is the degree of the function.
How do we move the function up 3 and 2 too the left?    answer



Cubic Function
f(x) = x3
How do you move a cubic function to the left, right or vertically? answer







Absolute Function
f(x) = |x|







Reciprocal Function
f(x) = 1/x

Why is the vertical axis a vertical asymptote?   answer







Square root Function
f(x) = √ x
Why does the graph begin at zero?
Could we alter the parent function to make the graph begin to the left of the vertical axis?
answer




Uses of parent functions.


return to PCTC