Asked by Jose
Describe the function resulting from reflecting f(x)=x^3+2x^2-x+5 about the y-axis and then shifting to the left by 4. Is this the same as performing the operations in the reverse order
Answers
Answered by
Steve
reflect: (x,y)->(-x,y)
f(x) -> -x^3+2x^2+x+5
shift: (x,y)->(x+4,y)
f(x) -> -(x+4)^3+2(x+4)^2+(x+4)+5
= -x^3-10x^2-31x-23
see the graphs here:
http://www.wolframalpha.com/input/?i=plot+y%3Dx^3%2B2x^2-x%2B5%2C+y%3D-x^3-10x^2-31x-23
the shift isn't real clear, but the reflection is.
f(x) -> -x^3+2x^2+x+5
shift: (x,y)->(x+4,y)
f(x) -> -(x+4)^3+2(x+4)^2+(x+4)+5
= -x^3-10x^2-31x-23
see the graphs here:
http://www.wolframalpha.com/input/?i=plot+y%3Dx^3%2B2x^2-x%2B5%2C+y%3D-x^3-10x^2-31x-23
the shift isn't real clear, but the reflection is.
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