5. For a given function ƒ(x) = x^5, a translation in the positive y-direction of two units is represented by which of the following? options:
A) ƒ(x + 2) = (x + 2)^5

B) ƒ(x + 2) = ( x – 2)^5

C) ƒ(x) – 2 = x^5 – 2

D) ƒ(x) + 2 = x^5 + 2

Step-by-step explanation:

Is the formula for upward vertical translation.

Is the formula for downward vertical translation.

Where is the units being translated.

Translation in the positive y-direction is upward vertical translation.

The translation is by 2 units.

The function becomes,

139 divided by a number

step-by-step explanation:

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.