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

The original function is k(x) = x^2. Provided that c cannot be equal to zero, we'll compare the following to the original position of the given function:

1. k(x+c) = (x+c)^2
The graph moves c units to the left is c is (+) and c units to the right if c is (-).

2. k(x) + c = x^2
The graph moves c units down when c is (+) and c units up when c is (-).

3. k(cx) = (cx)^2
Regardless of the sign, the graph becomes more narrow compared to the original if c is less than -1 and greater than 1, and becomes wider compared to the original if c is between -1 and 1 (if c is equal to zero, the graph becomes a line with equation y = 0).

By the way I can't understand the last (the c • k(x)). ^^;
Hope this helps~ :3

Answer 2

Given the function k(x) =x^2, 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(cx) c times k(x).