Answer:
The function f(x) is shifted 2 units to the left and 3 units up
Step-by-step explanation:
* Lets revise the translation of a function
- 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
∵ g(x) = x² + 3
∵ f(x) = g(x + 2)
- Lets find g(x + 2) by replacing x in g(x) by (x + 2)
∵ g(x) = x² + 3
∴ g(x + 2) = (x + 2)² + 3
∵ f(x) = g(x + 2)
∴ f(x) = (x + 2)² + 3
- The parent function of f(x) is x²
∵ x² changed to (x + 2)²
- Use the rules above
∴ f(x) is translated 2 units to the left
∵ (x + 2)² added by 3
- Use the rules above
∴ f(x) is translated 3 units up
* The function f(x) is shifted 2 units to the left and 3 units up
