Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Consider the function,

f(1) = 21 - 6

Match each transformation of Rx) with its description.

g() = 21 – 10

9(0) = 21 - 14

g(1) = 81 - 4

g(t) = 21 - 2

g(1) = 81 - 24

g(I) = 85 - 6

shifts 1x) 4 units right

stretches x) by a factor

of 4 away from the x-axis

compresses (x) by a factor

of 4 toward the y-axis

shifts x 4 units down

Answer 1

Shift 4 units down:
`g(x) = 2x - 10`

Stretching f(x) by 4 :
`g(x) =8x - 24`

Shift 4 units left:
`g(x) = 2x - 14`

Compress by 1/4 units :
`g(x) = 8x - 6`

Explanation:

Given

`f(x) = 2x - 6`

Required

Match the transformations (See attachment)

Shift 4 units down

Shifting down a function is represented as:

`g(x) = f(x) - b`

In this case:

`b = 4`

Substitute expression for f(x) and 4 for b in
`g(x) = f(x) - b`

`g(x) = 2x - 6 - 4`

`g(x) = 2x - 10`

Stretching f(x) by 4

Stretching a function by some units is represented as:

`g(x) =b.f(x)`

In this case:

`b = 4`

Substitute expression for f(x) and 4 for b in
`g(x) =b.f(x)`

`g(x) =4 * (2x - 6)`

`g(x) =8x - 24`

Shift 4 units left

Shifting a function to the left is represented as:

`g(x) = f(x - b)`

In this case:

`b = 4`

Substitute expression for f(x) and 4 for b in
`g(x) = f(x - b)`

`g(x) = f(x-4)`

Calculating f(x - 4)

`f(x) = 2x - 6`

`f(x - 4) = 2(x - 4) - 6`

`f(x - 4) = 2x - 8 - 6`

`f(x - 4) = 2x - 14`

Hence:

`g(x) = 2x - 14`

Compress by 1/4 units

This means that the function is stretched by
`1/(1)/(4)`

Compressing a function is represented as:

`g(x) =f(bx)`

In this case:

`b = 1/(1)/(4)`

`b = 1 * (4)/(1)`

`b = 4`

Substitute expression for f(x) and 4 for b in
`g(x) =f(bx)`

`g(x) =f(4x)`

Calculating f(4x)

`f(4x) = 2(4x) - 6`

`f(4x) = 8x - 6`

Hence:

`g(x) = 8x - 6`