The transformation of a function may involve any change. The function of the g(x) can be written as 3x². The correct option is C.
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units, y=f(x+c) (same output, but c units earlier)
- Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f(\dfrac{x}{k})
Given that f(x)=x², since the function g(x) is also similar to f(x), therefore, both the function are quadratic functions.
Since f(x) is streched vertically to form g(x), therefore, the function g(x) in terms of f(x) can be written as,
g(x) = k × f(x)
y = k × x²
Also, it is passing through the point (1,3), therefore, we can write,
3 = k × (1)²
3 = k
Thus, the function of the g(x) can be written as 3x².
Hence, the correct option is C.
Learn more about Transforming functions:
https://brainly.com/question/17006186
#SPJ2
