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02.02.2020 •
Mathematics
The function g(x)=x^2+3. the function f(x)=g(x+2). the function f(x) is shifted horizontally how many places to where ? the function f(x) is shifted vertically how many places where ?
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Ответ:
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
Ответ:
2000
Step-by-step explanation:
:)