SOLUTION: Graph h(x)= (x-1)^3+2 and explain how the graph shifts from the graph of f(x)=x^3, first to g(x)=(x-1)^2 and then to h(x)= (x-1)^3+2

Algebra ->  Rational-functions -> SOLUTION: Graph h(x)= (x-1)^3+2 and explain how the graph shifts from the graph of f(x)=x^3, first to g(x)=(x-1)^2 and then to h(x)= (x-1)^3+2      Log On


   

Question 1101015: Graph h(x)= (x-1)^3+2 and explain how the graph shifts from
the graph of f(x)=x^3, first to g(x)=(x-1)^2 and then to
h(x)= (x-1)^3+2
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
You are studying about the question:
 
"When you alter the equation, how does that alter the graph?"

Here is the graph of f%28x%29=x%5E3 in red:

graph%28300%2C400%2C-2%2C3%2C-4%2C4%2Cx%5E3%29

Next we take the right side of f(x), which is x3 and
replace x by x-1 and call it g(x).  That graph has the exact same
shape as the graph of f(x) except that it is shifted 1 unit to the
right of f(x).  Its graph is in green below, the graph of

g%28x%29=%28x-1%29%5E3

graph%28300%2C400%2C-2%2C3%2C-4%2C4%2Cx%5E3%2C%28x-1%29%5E3%29

Finally we take the right side of g(x), which is (x-1)3 and
add +2 and call it h(x).  That graph has the exact same shape as the 
graph of g(x), except that it is shifted (raised) 2 unit upward.  Its 
graph is in blue below, the graph of

h%28x%29+=+%28x-1%29%5E3%2B2 

graph%28300%2C400%2C-2%2C3%2C-4%2C4%2Cx%5E3%2C%28x-1%29%5E3%2C%28x-1%29%5E3%2B2%29

All three graphs have the same shape.

Edwin