Horizontal translations (hh) and vertical translations (cc) of a function have the form y=(x-h)2+cy=(x−h)2+c where the point (h,c)(h,c) is the vertex on the function. Horizontal translations have the opposite sign as the direction of their shift.
(-h)→ Shift Right
(+h)← Shift Left
To obtain the equation of the function by using y=x2, shift the graph to the right by 2 units. Remember squared functions have the form y=(x-h)2+c.
This shift is a horizontal translation (h) where h=-2 inside the brackets.
y=
x2
Write the new equation using y=x2 and h=-2. Remember horizontal translations have the opposite sign as the direction of their shift and squared functions have the form y=(x-h)2+c.
y=
(x-2)2
y=(x-2)2
Question 2 of 6
2. Question
Find the equation of the function when y=logx is shifted (translated) to the left by 5 units and down by 2 units.
Horizontal translations (h) and vertical translations (c) of a function here is in the form of y=log(x-h)+c where the point (h,c) is on the function. Horizontal translations have the opposite sign as the direction of their shift.
(-h)→ Shift Right
(+h)← Shift Left
(-c)↓ Shift Down
(+c)↑ Shift Up
To obtain the equation of the function by using y=logx, first shift the graph to the left by 5 units.
This shift is a horizontal translation left, where h=+5 inside the brackets.
Next, shift the graph down by -2 units.
This shift is a vertical translation (c) where c=-2.
y=
logx
Write the new equation using y=logx, c=-2, and h=+5. Remember horizontal translations have the opposite sign as the direction of their shift.
y=
log(x+5)-2
y=log(x+5)-2
Question 3 of 6
3. Question
Find the equation of the function when x2+y2=9 is shifted (translated) to the right by 2 units and up by 3 units.
Horizontal translations (h) and vertical translations (c) for a circle have the form (x-h)2+(y-c)2=r2 where the point (h,c) is the center. Horizontal and vertical translations for circles have the opposite sign as the direction of their shift.
(-h)→ Shift Right
(+h)← Shift Left
(-c)↑ Shift Up
(+c)↓ Shift Down
To obtain the equation of the function by using x2+y2=r2, first shift the graph to the right by 2 units. Remember circle equations have the form (x-h)2+(y-c)2=r2.
This shift is a horizontal translation (h) (2 units to the right) where h=-2 inside the brackets.
Next, shift the graph vertically up by 3 units where c=-3 inside the brackets.
x2+y2=
9
Since it’s in the form (x-h)2+(y-c)2=r2, then (x-2)2+(y-3)2=9.
Remember with circles, that the vertical and horizontal translations have the opposite sign since they are inside the brackets.
(x-2)2+(y-3)2=
9
(x-2)2+(y-3)2=9
Question 4 of 6
4. Question
Find the equation of the function when y=√x is shifted (translated) to the left by 2 units and up by 4 units.
Horizontal translations (h) and vertical translations (c) for a square root function has the form y=√x-h+c where the point (h,c) is the vertex for this function. Horizontal translations have the opposite sign as the direction of their shift.
(-h)→ Shift Right
(+h)← Shift Left
(-c)↓ Shift Down
(+c)↑ Shift Up
To obtain the equation of the function by using y=√x, first shift the graph to the left by 2 units. Remember square root functions have the form y=√x-h+c.
This shift is a horizontal translation (h) where h=+2 inside the square root.
Next, shift the graph up by 4 units (c=4)
y=
√x
Write the new equation using y=√x, c=4, and h=+2. Remember horizontal translations have the opposite sign as the direction of their shift.
y=
√x+2+4
y=√x+2+4
Question 5 of 6
5. Question
Find the equation of the function when y=1x is shifted (translated) to the left by 3 units and up by 2 units.
Horizontal translations (h) and vertical translations (c) for a hyperbolic function is in the form y=1x-h+c where (h,c) is the origin for this function. Horizontal translations have the opposite sign as the direction of their shift.
(-h)→ Shift Right
(+h)← Shift Left
(-c)↓ Shift Down
(+c)↑ Shift Up
To obtain the equation of the function by using y=1x, first shift the graph to the left by 3 units. Remember hyperbolas have the form y=1x-h+c.
Firstly, we shift a horizontal translation (left), where h=+3 in the denominator.
Next, shift a vertical translation up by 2 units (c=2).
y=
1x
Write the new equation using y=1x, c=2, and h=+3. Remember horizontal translations have the opposite sign as the direction of their shift and hyperbolas have the form y=1x-h+c.
y=
1x+3+2
y=1x+3+2
Question 6 of 6
6. Question
Find the equation of the function when y=2x-2 is shifted (translated) to the left by 3 units and up by 4 units.
Horizontal translations (h) and vertical translations (c) for an exponential function have the form y=2x-h+c where the point (h,c) is on the function. Horizontal translations have the opposite sign as the direction of their shift.
(-h)→ Shift Right
(+h)← Shift Left
(-c)↓ Shift Down
(+c)↑ Shift Up
To obtain the equation of the function by using y=2x-2, first shift the graph to the left by 3 units. Remember exponential functions have the form y=2x-h+c.
This shift is a horizontal translation (left), where h=+3.
Next, is a vertical translation up by 4 units (c=4).
y=
2x-2
Write the new equation using y=2x-2, c=4, and h=+3. Remember horizontal translations have the opposite sign as the direction of their shift and exponential functions have the form y=2x-h+c.