Question

Medal/Fan

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(x+c)

k(x)+c

k(cx)

ck(x)

Answer 1

if the original function was k(x) = x^2 then k(x)=x2k(x)+c⟹x2+cvertical shift upwards by "c"k(cx)⟹(c⋅x)2⟹c2⋅x2vertical shrink by a factor of c2c⋅k(x)⟹c⋅x2vertical shrink by a factor of "c"

Answer 2

uhhh....i dont get it

Answer 3

k(x) = x^2
k(x+c) is replacing x by (x+c).
This is equivalent to shifting k(x) to the LEFT by c units.
Replacing x by x -c will be shifting k(x) to the right by c units.

Answer 4

In the discussion above and below it is assumed c is positive.

k(x)+c shifts k(x) UP by c units. k(x) - c shifts k(x) down by c units.

k(cx) stretches or compresses k(x) horizontally.
if c is a fraction, that is 0 < c < 1, then it is a horizontal stretching. k(cx) will look wider compared to k(x) when c is a fraction.
if c > 1, it is a horizontal compression. k(cx) will look narrower compared to k(x) when c > 1.

Answer 5

ck(x) does vertical stretching or compression.
if c is a fraction, that is 0 <c < 1 the graph is compressed vertically
If c > 1, the graph is stretched vertically.

Answer 6

Thank you @ranga