translating functions

Question

Determine the equation of g(x) that results from the translating the function f(x)=x^2 +1 upward 5 units

 

A. g(x)=(x+6)^2

B. g(x) =(x+5)^2+1

C. g(x)=x^2-4

D. g(x)=x^2+6

 

I believe it is B. I did not even get close to any of the other answers. Is this correct or did I do this wrong? Please help

 

Answer 1

Translating upward 5 units means that the x coordinates are still the same and only the y coordinates are changing. 

 

This is a basic parabola with vertex at (0,1)   If it is translated upward it has not changed the shape of the parabola so it is still x^2 now just 5 more units up the y-axis. 

 

1+5 =6  so D. g(x)=x^2 + 6

 

D is the correct answer. Translating upward and downward only affects the constant term.

Answer 2

Keep in mind that when x=0 g(x)=1 for the original function. The y intercept on a function that has been translated up by 5 will need to be 6.  From this you can see you can see that g(x) or y must have 5 added to it for an upwards translation by five and g(x)+5=(x^2+1)+5 or g(x)+5=x^2+6, which is D.

Answer 3

Hi Christine;

The Answer is D.

f(x)=x²+1

Up five units...

g(x)=f(x)+5

g(x)=x²+1+5

g(x)=x²+6