Answer:
The function is a linear function
The function is translated 3 units to the left,then stretched vertically
by factor 2, then translated 5 units down
Step-by-step explanation:
* Lets revise some transformation
- 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
- If the function f(x) stretched vertically, then g(x) = k · f(x), where
k > 1 (multiplying each of its y-coordinates by k)
- If the function f(x) compressed vertically, then g(x) = k · f(x), where
0 < k < 1 (multiplying each of its y-coordinates by k)
* Now lets solve the problem
∵ f(x) = 2(x + 3) - 5
- The greatest power of the function is 1 (degree of the function)
∴ f(x) is linear function
- The parent function f(x) = x
∵ f(x) changed to f(x + 3)
∴ f(x) translated 3 units to the left
# Each x-coordinate of the points on the function subtracted by 3
∵ f(x + 3) changed to 2f(x + 3)
∵ 2 > 1
∴ f(x + 3) stretched vertically by factor 2 (k = 2)
# Each y-coordinate of the points on the function multiplied by 2
∵ 2f(x + 3) changed to 2f(x + 3) - 5
∴ 2f(x + 3) translated 5 units down
# Each y-coordinate of the points on the function subtracted by 5
