Question

Write the absolute value equation given the transformations

shifts right 5 units
shifts up 2 units
is reflected
is stretched by 0.5

Answer 1

y = - 0.5 | x - 5 | + 2

Explanation:

g(x) = |x|

`1^(st)` step - shifts right 5 units: g(x + 5) = | x - 5 |

`2^(nd)` step - shifts up 2 units: g(x + 5) + 2 = | x - 5 | + 2

`3^(rd)` step - reflected: - g(x + 5) + 2 = - | x - 5 | + 2

`4^(th)` step - stretched by 0.5: y = - 0.5 | x - 5 | + 2

y = - 0.5 | x - 5 | + 2