1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zielflug [23.3K]
3 years ago
13

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
LIst 3 words used in real life that indicate negative numbers.<br> plz help!!
larisa [96]
So you have 
1. Low money account balance
2. Negative degrees
3. Possible points in a game. 
8 0
3 years ago
True or False: You can tell if two ratios form a proportion if their cross products are equal. True O False​
daser333 [38]

Answer:

Step-by-step explanation:

False

7 0
3 years ago
I need help finding y
kolezko [41]

to solve for y, we must multiply by t on both side to get ride of the t in the denominator. By doing this, we will get:

{t}^{3}

on the right side.

Subtracting 3, and we have successfully isolated y.

It would be impossible to get a quantitative value for y if we don't know the value of t.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Adam invested $12,000 in a six-year CD that paid 7.1% interest, but later needed to withdraw $2,500 early. If the CD's penalty f
    9·1 answer
  • Which logic statement represents this argument?<br><br> PLEASE HELP WILL MARK BRAINLIEST!!!
    7·2 answers
  • Help me with this one please!!!!!!!!
    14·2 answers
  • How many times can 4 go into 724
    14·2 answers
  • A bike and skate shop rents bikes for $21 per day and pairs of skates for $20 per day. To remain viable, the shop needs to make
    15·1 answer
  • A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says,
    5·2 answers
  • PLEASE HELP, 50 POINTS! This is a triangle investigation.
    6·2 answers
  • The measure of an angle is seventeen times the measure of a complementary angle. What is the measure of each angle?
    7·1 answer
  • The equation of the line of best fit of a scatterplot is y = -8x + 3. What is the y-intercept?
    10·1 answer
  • Any suggestions for concentrating on schoolwork?<br> Don't answer unless you have serious advice
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!