Write two linear functions, f(x) and g(x). for example, f(x)= 3x-7 and g(x)= -2x+5. then see whether f(x) - (-g(x)) is equivalent to f(x) + g(x).

the two expressions are equivalent.

Step-by-step explanation:

We know that f(x)= 3x-7 and g(x)= -2x+5, therefore:

f(x) - (-g(x)) = 3x-7 - ( +2x-5) = 3x - 7 - 2x + 5 = x -2

f(x) + g(x) = 3x-7 -2x + 5 = x - 2

Therefore,  f(x) - (-g(x)) is equivalent to f(x) + g(x).

Another way to check that the two expressions are equivalent is by solving the parenthesis:

f(x) - (-g(x)) →  f(x) + g(x)

Therefore, the two expressions are equivalent.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.