Transformations Review

Transformation Rules

100

f(x)+b

How does b transform the function?

Shift Up

200

f(x-b)

How does b transform the function?

Shift Right

300

-f(x)

How is the function being transformed?

Reflected over the x-axis

400

f(-x)

How is the function being transformed?

Reflection across the y-axis

500

af(x)

How does a transform the function when greater than 1?

How does a transform the function when less than 1?

Greater than 1 - Vertical stretch (taller/more steep)

Less than 1 - Vertical shrink (Shorter/less steep)

Name the Transformation

100

f(x-2)+3

Right 2; Up 3

200

1/2f(x)

Vertical Shrink of 1/2

300

-f(x+3)-7

Left 3; Down 7; Reflect over x-axis

400

f(-1/4x)-3

Down 3; Reflect over y-axis; Horizontal stretch of 1/4

500

-3f(-x+2)-5

Left 2; Down 5; Reflect of x-axis; Reflect over y-axis; Vertical Stretch of 3

Graphs

100

Graph 1 

f(x+1)+2

200

Graph 2

f(x-3)-1

300

Graph 3

-f(x+4)-1

400

Graph 4

-f(x-2)+5

500

Graph 5

f(x-2)+3

Even & Odd

100

Graph 1

Even

200

Graph 2

Odd

300

Graph 3

Neither

400

3x²+x⁴

Even

500

2x⁵-3

Neither

Write the Equation

100

A function being shifted up 3

f(x)+3

200

A function being reflected over the y-axis; shifted right 5; down 2

f(-x-5)-2

300

A function being horizontally stretched by a scale of 1/4; shifted down 3, right 4

f(1/4x-4)-3

400

A function being shifted up 5; reflected over the x-axis; and vertically stretched by a scale of 2

-2f(x)+5

500

A function being reflected over the x-axis; reflected over the y-axis; shifted left 5; down 4

-f(-x+5)-4