Question

This is a big question i am stuck on and need help with... anyone want to help me?? :/

Recall that each family of functions has a simplest function called the parent function.
A) Compare the graphs of y = x3 and y = x3 - 4. Describe how the graph of y = x3 - 4 relates to the graph of y = x3.
B) Compare the graphs of y = x3 and y = 1/4 x3. Describe how the graph of y = 1/4 x3 relates the the graph of y = x3.

Answer 1

These are easier than they seem, once you get used to the terminology used.

Answer 2

Really? Well for me i am like "whaaat?" :)

Answer 3

Let's take a simple example, y=x, the identity function, is the parent function of any straight line, especially any straight line with a slope of 1.

Answer 4

y=x^2, the squaring function, is the parent of all quadratic equations.
The various 'daughter functions' that are formed from the parent function are due to various transformations: translations up/down or left/right, reflections about an axis (usually flipping it upside down across the x-axis), or amplifications/reductions.

In the y=x^2 example, I could transform it by shifting it up 5 units -> y=x^2+5. or I could translate it 3 units left -> y=(x+3)^2, etc.

Answer 5

okay.. so i understand it in your example... in my question the -4 would be shifting it left because of the negative? or?

Answer 6

The -4 is affecting the y, so that is a shift down.

Answer 7

oh i see okay

Answer 8

imagine if x=0, y=-4, where as in the parent function if x=0, y=0, so the new function is the same only 4 units down.

Answer 9

Probably the best way to get a handle on these is to actually graph them and look at them, and experiment with different scenarios, e.g. 'what happens to y if I do this to x?' 'what happens to x if I do this to y,' etc.

Answer 10

okey (: