The sum and product of two linear functions are shown. Which statements can be used to describe the original functions f(x) and g(x)? Select three options.

When added, the sum of the y-intercepts must be 8.
When multiplied, the product of the y-intercepts must be 8.
Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
f(x) could have a rate of change equal to 3 and g(x) could have a rate of change of –3.
f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –1.

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.

i need a picture

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.