Horizontal translations (shifts) of functions are written in the form y=f(x+h).
h is how many units right or left the graph will be shifted.
(-h)→ Shift Right
(+h)← Shift Left
To find the equation of the graph on the right of f(x)=x3–2x2+x, count the number of units the graph is shifted over.
Count the number of units the graph is shifted over to the right.
The graph is shifted by 2 units.
Using the form y=f(x+h) for horizontal translations and remembering that a shift to the right means h is negative, the formula for the new graph to the right is f(x)=(x-2)3–2(x-2)2+(x-2)
Then, we simplify the function by using the distributive property.
f(x)
=
(x-2)3–2(x-2)2+(x-2)
=
(x-2)(x-2)(x-2)-2(x-2)(x-2)+(x-2)
=
(x-2)(x2-4x+4)-2(x2-4x+4)+(x-2)
=
x3–4x2+4x–2x2+8x–8-2x2+8x–8+x–2
=
x3–8x2+21x-18
Combining similar terms
Therefore, our simplified formula for the new graph to the right is f(x)=x3–8x2+21x-18
Question 2 of 5
2. Question
Find the equation of the graph on the left of f(x)=x2
Horizontal translations (shifts) of functions are written in the form y=f(x+h).
h is how many units right or left the graph will be shifted.
(-h)→ Shift Right
(+h)← Shift Left
To find the equation of the graph on the left of f(x)=x2, count the number of units the graph is shifted over.
Count the number of units the graph is shifted over to the left.
The graph is shifted by 3 units.
Using the form y=f(x+h) for horizontal translations and remembering that a shift to the left means h is positive, the formula for the new graph to the left is f(x)=(x+3)2
Question 3 of 5
3. Question
Find the equation of the graph on the left of f(x)=√x
Horizontal translations (shifts) of functions are written in the form y=f(x+h).
h is how many units right or left the graph will be shifted.
(-h)→ Shift Right
(+h)← Shift Left
To find the equation of the graph on the left of f(x)=√x, count the number of units the graph is shifted over.
Count the number of units the graph is shifted over to the left.
The graph is shifted by 4 units.
Using the form y=f(x+h) for horizontal translations and remembering that a shift to the left means h is positive, the formula for the new graph to the left is f(x)=√x+4
Question 4 of 5
4. Question
Find the equation of the graph on the right of f(x)=2x
Horizontal translations (shifts) of functions are written in the form y=f(x+h).
h is how many units right or left the graph will be shifted.
(-h)→ Shift Right
(+h)← Shift Left
To find the equation of the graph on the left of f(x)=2x, count the number of units the graph is shifted over.
Count the number of units the graph is shifted over to the right.
The graph is shifted by 3 units.
Using the form y=f(x+h) for horizontal translations and remembering that a shift to the right means h is negative, the formula for the new graph to the right is f(x)=2x-3
Question 5 of 5
5. Question
Find the equation of the graph on the right of f(x)=|x+2|
Horizontal translations (shifts) of functions are written in the form y=f(x+h).
h is how many units right or left the graph will be shifted.
(-h)→ Shift Right
(+h)← Shift Left
To find the equation of the graph on the left of f(x)=|x+2|, count the number of units the graph is shifted over.
Count the number of units the graph is shifted over to the right.
The graph is shifted by 5 units.
Using the form y=f(x+h) for horizontal translations and remembering that a shift to the right means h is negative, the formula for the new graph to the left is f(x)=|x+2-5| or simply f(x)=|x–3|
