Respuesta :

Answer:

a). g(x) = f(x - 2) - 1

b). f(x) = g(x + 2) + 1

Step-by-step explanation:

From the graph attached,

There are two observations:

1). Function 'f' has been shifted by 2 units right and 1 unit down to form image function 'g'.

2). Function 'g' has been shifted 2 units left and 1 unit up to form image function 'f'.

Equation of the quadratic function 'f' is,

f(x) = x²

Equation of function 'g'.

g(x) = (x - 2)² - 1

Therefore, both the functions can be defined as,

a). g(x) = f(x - 2) - 1

b). f(x) = g(x + 2) + 1

a) The function formula for g using the function f is g(x) = f(x - 2) - 1

b) The function formula for f using the function g is f(x) = g(x + 2) + 1

Calculation of the function formula:

1). Function 'f' should be shifted by 2 units right and 1 unit down to form image function 'g'.

2). Function 'g' should be shifted 2 units left and 1 unit up to form image function 'f'.

So,

Equation of the quadratic function 'f' is,

f(x) = x²

And,

Equation of function 'g'.

g(x) = (x - 2)² - 1

Therefore, both the functions can be defined as,

a). g(x) = f(x - 2) - 1

b). f(x) = g(x + 2) + 1

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