I missed a class a while back and now i'm studying for finals and realized that I have no idea how to do this cause it was the class I missed... so I'll just post the question.....
the function f(x)=x^2 is transformed as follows:
- vertical expansion by a factor of 2
-reflected in the x-axis
- translated 3 units left and 5 units up
write the equation of the transformed function.
(if you could try to explain what to do so I actually understand it that would be nice too...)
thanks ahead of time!
the function f(x)=x^2 is transformed as follows:
- vertical expansion by a factor of 2
-reflected in the x-axis
- translated 3 units left and 5 units up
write the equation of the transformed function.
(if you could try to explain what to do so I actually understand it that would be nice too...)
thanks ahead of time!
-
f(x)=x^2 or y = x^2 and f(x) = y
- vertical expansion by a factor of 2:
It means expand along the y-axis. In other word, multiply y by 2
so:
f(x) = 2y = 2 x^2
- reflected in the x-axis
reflect of mirror with x-axis, means
f(x) = -y = - 2 x^2
- translated 3 units left
the new x will be x+3
f(x) = - 2 (x+3)^2
- and 5 units up
the new y will be y+5
f(x) = y + 5 = (- 2 (x+3)^2) +5
= -2 x^2 - 12x - 18 + 5
= -2 x^2 -12x - 13
- vertical expansion by a factor of 2:
It means expand along the y-axis. In other word, multiply y by 2
so:
f(x) = 2y = 2 x^2
- reflected in the x-axis
reflect of mirror with x-axis, means
f(x) = -y = - 2 x^2
- translated 3 units left
the new x will be x+3
f(x) = - 2 (x+3)^2
- and 5 units up
the new y will be y+5
f(x) = y + 5 = (- 2 (x+3)^2) +5
= -2 x^2 - 12x - 18 + 5
= -2 x^2 -12x - 13