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(cx)
c • k(x)

Answer 1

@ranga

Answer 2

btw i know that k(cx) controls how wide or narrow the graph is. is that correct?

Answer 3

yes.

Answer 4

ok so how about the second function?

Answer 5

thats where i got stuck

Answer 6

k(x) = x^2 (It is a parabola. It opens upwards)
First one: k(cx) = (c^2)x^2 (This is also a parabola. c^2 is always positive whether c is negative or positive and therefore this parabola also opens upwards. The value of c^2 will determine how narrow or wide the parabola will be. discus the case of |c| < 1 and |c| > 1

Answer 7

k(x) = x^2 (It is a parabola. It opens upwards)
Second case: c * k(x) = cx^2.
cx^2 is also a parabola. If c is negative, the parabola will open downward.
If c is positive the parabola will open upward.
Discuss two possibilities: |c| < 1 and |c| > 1

Answer 8

ohh i see

Answer 9

so for the first it controls how WIDE the parabola will be. the second one controls whether the parabola will open UPWARD or DOWNWARD

Answer 10

In the first case, k(cx), will compress or stretch the graph horizontally.
If |c| < 1 (that is, a fraction) the graph will be stretched horizontally.
If |c| > 1 the graph will be compressed horizontally.

Answer 11

could you sketch if please?

Answer 12

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