Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.

Mathematics

1 answer:

Reptile [31]3 years ago

5 0

Answer:

asymptotes: x = -4, x = 4
zeros: x = 0

Step-by-step explanation:

The vertical asymptotes of the rational expression are the places where the denominator is zero:

x^2 -16 = 0

(x -4)(x +4) = 0 . . . . . true for x=4, x=-4

x = 4, x = -4 are the equations of the vertical asymptotes

The zeros of a rational expression are the places where the numerator is zero:

4x = 0

x = 0 . . . . . . divide by 4

You might be interested in

The graph of y=f(x) is the solid black graph below. Which function represents the dotted graph?

Fed [463]

Answer: y = f(x - 4) - 1, lower left corner

=============================================================

Explanation:

Let's focus on only the left-most points of each curve

For the black semicircle, the left-most point is located at (-7,0). The corresponding point on the red semicircle is at (-3,-1)

To go from (-7,0) to (-3,-1), we will do two things

Shift 4 units to the right
Shift 1 unit down

This can be done in any order. The action of "shift 4 units to the right" is effectively the same as shifting the xy axis 4 units to the left while keeping the curves fixed in place. This gives the illusion of movement. When we shift 4 the xy axis 4 units to the left, we're replacing each x input with x-4 as the new input.

In short, we go from f(x) to f(x-4). This is why we have this opposite motion going on.

The up and down motion is fairly straight forward. To shift 1 unit down, we subtract off 1. This is to subtract 1 from the y coordinate.

Overall, we go from y = f(x) to y = f(x - 4) - 1

Applying this transformation will move (-7,0) to (-3,-1) as described above. It will also move every other point on the black curve to their new corresponding location on the red curve.

3 0

3 years ago

Help me find x it’s really hard

Vilka [71]

Answer:

x = 140

Step-by-step explanation:

180 - 65 - 75= 40

180 - 40 = x

140 = x

3 0

3 years ago