Question

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

Consider the function.
f(x) = 2x - 6

Answer 1

1) shifts f(x) 4 units down = g(x) =
`2x-10`

2) stretches by factor 4 = g(x) =
`8x-24`

3) shifts f(x) 4 units right = g(x) =
`2x-14`

4) compresses by factor 4 = g(x) =
`8x-6`

Explanation:

1) When we have to move the function down by 4 units, subtract the whole function by -4, that is y -4.

Thus, f(x) becomes g(x) =
`2x-6-(4)` =
`2x-10`

2) When the function is stretched away from x axis, it means in Y direction.

Thus, when stretched 4 units in Y direction, the function becomes 4(f(x))

= g(x) =
`4(2x-6)` =
`8x-24`

3)When we have to move the function right by 4 units, replace x with (x-4) in the function.

Thus, f(x) becomes g(x) =
`2(x-4)-6` =
`2x-8-6` =
`2x-14`

4) When the function is stretched towards y axis, it means in X direction.

Thus, when compressed 4 units in X direction, replace the x by 4x.

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