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
adell [148]
2 years ago
7

(01.03. 106, 1.08 HC)

Mathematics
1 answer:
zlopas [31]2 years ago
7 0

Answer:

  A) see attached for a graph. Range: (-∞, 7]

  B) asymptotes: x = 1, y = -2, y = -1

  C) (x → -∞, y → -2), (x → ∞, y → -1)

Step-by-step explanation:

<h3>Part A</h3>

A graphing calculator is useful for graphing the function. We note that the part for x > 1 can be simplified:

  \dfrac{-x^2+x+2}{x^2-3x+2}=-\dfrac{(x-2)(x+1)}{(x-2)(x-1)}=-\dfrac{x+1}{x-1}\quad x\ne 2

This has a vertical asymptote at x=1, and a hole at x=2.

The function for x ≤ 1 is an ordinary exponential function, shifted left 1 unit and down 2 units. Its maximum value of 3^-2 = 7 is found at x=1.

The graph is attached.

The range of the function is (-∞, 7].

__

<h3>Part B</h3>

As we mentioned in Part A, there is a vertical asymptote at x = 1. This is where the denominator (x-1) is zero.

The exponential function has a horizontal asymptote of y = -2; the rational function has a horizontal asymptote of y = (-x/x) = -1. The horizontal asymptote of the exponential would ordinarily be y=0, but this function has been translated down 2 units.

__

<h3>Part C</h3>

The end behavior is defined by the horizontal asymptotes:

  for x → -∞, y → -2

  for x → ∞, y → -1

You might be interested in
Many people who bought Z-Game gaming systems over the holidays have complained that the systems they purchased were defective. I
Bas_tet [7]

Answer:

The upper limit for the 95% confidence interval for the population proportion of defective gaming systems is 0.022

Step-by-step explanation:

Upper Limit for 95% Confidence Interval can be calculated using p+ME where

  • p is the sample proportion of defective gaming systems (\frac{18}{1200} = 0.015)
  • ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} } where

  • z is the statistic of 95% confidence level (1.96)
  • p is the sample proportion (\frac{18}{1200}=0.015
  • N is the sample size (1200)

Using the numbers we get:

ME=\frac{1.96*\sqrt{0.015*0.985}}{\sqrt{1200} } ≈ 0.007

Then upper limit for the population proportion is 0.015+0.007 =0.022

4 0
3 years ago
A taxi driver charges $3 for every kilometre driven, plus $4 per trip.
Stels [109]
Last one is the answer pretty sure
6 0
3 years ago
Solve by substitution 3x+4y=10<br>y=-2x+10​
mixer [17]

Answer:

Plug in and solve

Step-by-step explanation:

6 0
3 years ago
(02.04 MC)
Ainat [17]

(\stackrel{x_1}{3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{18}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{18}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{ 12 }{ 2 } \implies 6

\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 6}(x-\stackrel{x_1}{3}) \\\\\\ y-6=6x-18\implies {\Large \begin{array}{llll} y=6x-12 \end{array}}

6 0
1 year ago
True or False- To find the area of a square you add the length of all 4 sides
aleksley [76]

Answer:

False

Step-by-step explanation:

To find the area of the square, you multiply length by length, adding the length of all 4 sides would be the perimeter

6 0
3 years ago
Read 2 more answers
Other questions:
  • A group of eight grade 11 and five grade 12 students wish to be on the senior prom committee. The committee will consist of thre
    8·1 answer
  • Ben dives from a 10-foot platform. The equation h = -16 t 2 + 27t + 10
    14·1 answer
  • Find and compare the median and
    5·1 answer
  • Carlos spent 1 1/4 hours doing his math homework he spent 1/4 of his time practicing his multiplication facts how many hours to
    7·2 answers
  • Simplify using the distributive property <br> -3(s – 1) + 5s.
    5·2 answers
  • Is the following relation a function? (1 point)
    11·2 answers
  • There are two packs of hyenas that live just outside of a small town in Harar, Ethiopia. Each night, the
    10·1 answer
  • –4.36 − 1.6g + 7.4 = 0.3g + 6.46
    5·1 answer
  • Can somebody help me with my social studies?
    7·1 answer
  • I need answer now please asap you will be marked as brainliest :D
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!