Describe a function that transforms the parent root function with a horizontal compression by a factor of 3 and a downward shift of 15 units.

g(x) = f(3x) -15

Step-by-step explanation:

Let f(x) be the parent function.

If the function is to be compressed by a factor of 3 horizontally, we must obtain the value f(3) when x=1, for example. We can do that by using 3x as the argument of the function:

  g(x) = f(3x)

If its graph is to be shifted downward by 15 units, every value produced by the function must have -15 added to it. That is, the shifted function is ...

  g(x) = f(3x) - 15

_____

The attached graph shows an example function compressed horizontally and vertically shifted.

,xzgv

step-by-step explanation:

; oqirjg'

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.