Question 1177624
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The 1/3 shrinks the graph vertically by a factor of 3 (i.e., "stretches" it by a factor of 1/3).<br>
The x+2 shifts the graph 2 units to the left.<br>
The -1 shifts the graph 1 unit down.<br>
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:<br>
first: simplify inside parentheses: x+2: shift left 2
second: multiplication/division: 1/3: shrink vertically
third: addition/subtraction: -1: shift down 1<br>
Parent function: x^3
{{{graph(400,400,-5,3,-50,50,x^3)}}}
first transformation: (x+2)^3: shift left 2
{{{graph(400,400,-5,3,-50,50,x^3,(x+2)^3)}}}
second transformation: (1/3)(x+2)^3: shrink by a factor of 3
{{{graph(400,400,-5,3,-50,50,x^3,(x+2)^3,(1/3)(x+2)^3)}}}
third transformation: (1/3)(x+2)^3-1: shift down 1
{{{graph(400,400,-5,3,-50,50,x^3,(x+2)^3,(1/3)(x+2)^3,(1/3)(x+2)^3-1)}}}