Find g, if f(x) = x^3, g is found by reflecting f, then....

[snakeyesxlaw]

Let f (x) = x^3.

The graph of a function g is created by
reflecting the graph of f in the x-axis
then shifting left 7 units
and finally shifting up 20.

Find the function g.

these are the two i came up with but know its wrong.

g(x) = (x^3+7)+20

or

g(x) = (x^3+7)^2+20

any suggestions?

 

[arthur ohlsten]

let y=x, then to reflect it about the x axis you would have :
reflection is y=-x
=============================================
y=x^3
reflection is y=-x^3

===========================================
y=x
to shift left 7 units replace x with [x-7]
reflection is : y=[x-7]

let y=x^3
reflect about x axis and shift left 7 units
y=-[x-7]^3

==================================================
y=x
shift up 20 units add 20
shifted up y=x+20

==================================================
y=x^3
reflect about x axis, shift left 7 units and up 20

y=-[x-7]^3+20 answer

Arthur

 

[stapel]

these are the two i came up with but know its wrong....

By what reasoning did you arrive at your answers?

Please be complete. Thank you!

Eliz.