SOLUTION: Describe a series of transformations from the parent function, f(x) = x^n that gives us g(x)= 1/3(x+2)^3 -1. Be sure the transformations are written in the proper order.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Describe a series of transformations from the parent function, f(x) = x^n that gives us g(x)= 1/3(x+2)^3 -1. Be sure the transformations are written in the proper order.       Log On


   

Question 1177624: Describe a series of transformations from the parent function, f(x) = x^n that gives us g(x)= 1/3(x+2)^3 -1. Be sure the transformations are written in the proper order.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The 1/3 shrinks the graph vertically by a factor of 3 (i.e., "stretches" it by a factor of 1/3).

The x+2 shifts the graph 2 units to the left.

The -1 shifts the graph 1 unit down.

The order of the transformations is the order in which you would apply the changes if you were evaluating the expression for a given value of x, using standard order of operations:

first: simplify inside parentheses: x+2: shift left 2
second: multiplication/division: 1/3: shrink vertically
third: addition/subtraction: -1: shift down 1

Parent function: x^3
graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%29
first transformation: (x+2)^3: shift left 2
graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%2C%28x%2B2%29%5E3%29
second transformation: (1/3)(x+2)^3: shrink by a factor of 3

third transformation: (1/3)(x+2)^3-1: shift down 1