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

This is a perfect question to answer using a graphing calculator like desmos. Have you ever heard of desmos?

Answer 2

yea but i don't understand it

Answer 3

@mathteacher1729

Answer 4

k(cx) = c^2x^2
c.k(x) = cx^2.

Answer 5

i need to know how it changes the graph

Answer 6

Go here: https://www.desmos.com/calculator
Type in your functions.

k(x) = x^2
f(x) = (c*x)^2
g(x) = c*(x)^2

Let c be a slider (there will be a button for it automatically when you type it).

Then slide c and see what happens! :)

Answer 7

for that you need to draw the graph. One will be more steeper than the other one. The slope of the tangent for the second one will be greater than the first one (i guess, you need to check by yourself by drawing the slope, but checking the slope of the tangent is the best way to analyze a curved function like this).

Answer 8

The graph will change automatically and you can see how it changes.

Answer 9

so for (c*x)^2, it controls how wide and narrow the graph is?

Answer 10

i slid the slider and it got wider and narrower

Answer 11

@mathteacher1729

Answer 12

and the c*(x)^2 controls whether it opens up or down?

Answer 13

Be sure to specify what happens in the following cases when:

-1 < c < 1
c = 1
c = -1
c < -1
and
c > 1

Answer 14

??? im lost sorry