Answer:
1. y = - 4(x - 1) ⇒ Translated right by 1 unit
2. y = 1 - 4x ⇒ Translated up by 1 unit
3. y = - 4(-x) ⇒ Reflected across the y-axis
4. y = - 4(x + 1) ⇒ Translated left by 1 unit
5. y = 4x ⇒ Reflected across the x-axis
6. y = -1 - 4x ⇒ Translated down by 1 unit
Step-by-step explanation:
Lets explain how to solve the problem
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Lets solve the problem
∵ y = - 4x is the parent function
- The function after some transformation is:
1. y = - 4(x - 1)
∵ We subtract 1 from x
∴ The function translated right by 1 unit
∴ y = - 4(x - 1) ⇒ Translated right by 1 unit
2. y = 1 - 4x
∵ We add 1 to y = - 4x
∴ The function translated up by 1 unit
∴ y = 1 - 4x ⇒ Translated up by 1 unit
3. y = -4(-x)
∵ We multiply x by (-)
∴ The function reflected across the y-axis
∴ y = - 4(-x) ⇒ Reflected across the y-axis
4. y = -4(x + 1)
∵ We add 1 to x
∴ The function translated left by 1 unit
∴ y = - 4(x - 1) ⇒ Translated left by 1 unit
5. y = 4x
∵ We multiply y = - 4x by (-)
∴ The function reflected across the x-axis
∴ y = 4x ⇒ Reflected across the x-axis
6. y = -1 - 4x
∵ We subtract 1 from y = - 4x
∴ The function translated down by 1 unit
∴ y = -1 - 4x ⇒ Translated down by 1 unit
