Algebra 1 1.6 and 1.7 (Transformations and Key Features)

Equation to Statement

100

f(x)+4

Vertical translation of 4 units (up)

200

2f(x-7)

Horizontal translation of 7 units (right), vertical dilation by factor of 2

300

f(x+5) + 1

Horizontal translation by -5 units (left) and vertical translation by 1 unit (up)

400

-f(3x)+2

Horizontal dilation by factor of 1/3, reflection over the x-axis, and vertical translation by factor of 2 (up)

500

3f(1/5 x)-2

horizontal dilation by factor 5, vertical dilation by factor 3, and vertical translation of -2 units (down)

Transformed Domain/Range

100

Which values of the formula will effect the domain? 

af(bx+h)+k

b and h. (multiply by 1/b and add -h)

200

Which values of the formula would effect the range? 

af(bx+h)+k

a and k. (multiply by a and add k)

300

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)

400

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

500

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)

Statement to Equation

100

What equation would match a function that goes down 5 units?

f(x)-5

200

What equation would transform a function left 8 units?

f(x+8)

300

What equation would transform a function with a vertical dilation of 2 and a horizontal translation of 6 left?

2f(x+6)

400

What equation would transform a function by horizontal dilation of 4 and up 1?

f(1/4 x) +1

500

What equation would transform a function with a reflection over the y-axis, vertical dilation of 1/2, and a vertical translation of 3 units down?

1/2 f(-x) -3

General Knowledge

100

What does the number +5 do in the function: 

-f(3x-7)+5

Vertical translation (up) of 5 units

200

What transformation happens with the value of b: f(bx)

Horizontal dilation by factor of 1/b

300

A negative in front of a function: -f(x), will do what?

Reflect over the x-axis

400

What would be the first transformation done to the function: 

2f(x-1)+5

Horizontal translation of 1 unit (right)

500

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)