Question

Given the function k(x) = x2, compare and contrast how the application of a constant, c, affects the graph. The application of the constant must be discussed in the following manners:

k(x + c)
k(x) + c
k(cx)
c • k(x)

Answer 1

shift or scale. Any ideas which go where?

Answer 2

i don't understand it can you

Answer 3

consider the graph

k(x) = x^2

k(x) = x^2+5 is the same graph, shifted up 5 units.

Similarly, k(x) = (x-5)^2 is the same graph, shifted to the right by 5 units.

If you think of the k-axis moved to the right 5 units, all the new x-coordinates are 5 less than the old ones. That's why substituting (x-5) is the same as moving the k-axis 5 units to the right.

Think of scaling the same way. The graph grows or shrinks because the x-coordinate grows or shrinks by a factor of c.

Visit http://rechneronline.de/function-graphs/ where you can play around with tweaking the functions and see how they are affected. You can display up to 3 graphs at once. So, enter

x^2 for the first,
(x-5)^2 for the 2nd, and
x^2+5 for the 3rd.

You might want to change x and y ranges from -5 to 5 and make them -10 to 10 instead. Just play around some.