Equation to Statement
f(x)+4
Vertical translation of 4 units (up)
Which values of the formula will effect the domain?
af(bx+h)+k
b and h. (multiply by 1/b and add -h)
What equation would match a function that goes down 5 units?
f(x)-5
What does the number +5 do in the function:
-f(3x-7)+5
Vertical translation (up) of 5 units
2f(x-7)
Horizontal translation of 7 units (right), vertical dilation by factor of 2
Which values of the formula would effect the range?
af(bx+h)+k
a and k. (multiply by a and add k)
What equation would transform a function left 8 units?
f(x+8)
What transformation happens with the value of b: f(bx)
Horizontal dilation by factor of 1/b
f(x+5) + 1
Horizontal translation by -5 units (left) and vertical translation by 1 unit (up)
If the range of a function is below, what would the new domain be for the function 2f(x)-3
0 < y <6
-3<y<9 (multiply by 2 then subtract 3)
What equation would transform a function with a vertical dilation of 2 and a horizontal translation of 6 left?
2f(x+6)
A negative in front of a function: -f(x), will do what?
Reflect over the x-axis
-f(3x)+2
Horizontal dilation by factor of 1/3, reflection over the x-axis, and vertical translation by factor of 2 (up)
If the domain of a function is shown below, what would the domain be of the function f(2x-7)?
-2<x<8
6<x<11 multiply by 1/2 and add 7
What equation would transform a function by horizontal dilation of 4 and up 1?
f(1/4 x) +1
What would be the first transformation done to the function:
2f(x-1)+5
Horizontal translation of 1 unit (right)
3f(1/5 x)-2
horizontal dilation by factor 5, vertical dilation by factor 3, and vertical translation of -2 units (down)
If the function has the domain of x>0 and range of y<1, what would the new domain and range be of the function below.
-f(1/3 x+1)-4
domain: x>-1 (0 multiply by 3 and subtract 1); domain: y>-5 (1 multiply by -1 and subtract 4 then flip sign because multiply with a negative)
1/2 f(-x) -3
What is the proper order of transformations of:
af(bx+h)+k
1/b (horizontal dilation), -h (horizontal translation), a (vertical dilaiton), then k (vertical translation)