Question

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

Answer 1

Answer:

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 : $g(x) = 8x - 6$

Step-by-step 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 $1/\frac{1}{4}$

Compressing a function is represented as:

$g(x) =f(bx)$

In this case:

$b = 1/\frac{1}{4}$

$b = 1 * \frac{4}{1}$

$b = 4$

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:

$g(x) = 8x - 6$