F(x) = 7^x

G(x) = 7^x + 6

Which statement about f(x) and its translation, g(x), is true ?

A). The domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}.

B). The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}.

C). The asymptote of g(x) is the asymptote of f(x) shifted six units down.

D). The asymptote of g(x) is the asymptote of f(x) shifted six units up.

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.

first one because it can't have a fraction in it

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240