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
IrinaVladis [17]
3 years ago
6

Domain and Range for the function f(x)=5IXI is

Mathematics
1 answer:
shutvik [7]3 years ago
7 0

Answer:

The domain of the function f(x) is:

\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:

The range of the function f(x) is:

\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}

Step-by-step explanation:

Given the function

f\left(x\right)=5\left|x\right|

Determining the domain:

We know that the domain of the function is the set of input or arguments for which the function is real and defined.  

In other words,  

  • Domain refers to all the possible sets of input values on the x-axis.

It is clear that the function has undefined points nor domain constraints.

Thus, the domain of the function f(x) is:

\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:

Determining the range:

We also know that range is the set of values of the dependent variable for which a function is defined.  

In other words,  

  • Range refers to all the possible sets of output values on the y-axis.

We know that the range of an Absolute function is of the form

c|ax+b|+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k

k=0

so

Thus, the range of the function f(x) is:

\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}

You might be interested in
How to do the equation for the sum of three consecutive integers is 467
Dvinal [7]
Call n, the first of those consecutive terms, then three consecutive terms are:n, n +1, and n +2.

So, the equation will be n + (n +1) + (n +2) = 467

=> n + n + 1 + n + 2 = 467

=> 3n + 3 = 467

All of them are valid forms of the equation for the sum of three consecutive integers is 467.

You can solve it now, if you want:

3n = 467 - 3

3n = 464

n = 464 / 3

n = 154.6

The solution means that there are not three consecutive numbers whose sume is 467.

You can verifiy that if you take 154 + 155 + 156 = 465

And 155 + 156 + 157 = 468
4 0
3 years ago
(4z^5 - 14z^4 + 10z^3 - 16z^2 + 41z - 2) / (z - 2)
r-ruslan [8.4K]

Answer:

4z4−6z3−2z2−20z+1

Step-by-step explanation:

4z5−14z4+10z3−16z2+41z−2

z−2

=

4z5−14z4+10z3−16z2+41z−2

z−2

=

(z−2)(4z4−6z3−2z2−20z+1)

z−2

=4z4−6z3−2z2−20z+1

(theres no more like terms so u cant)

4 0
2 years ago
Pleasee help, thank you so much
dezoksy [38]

Answer:

-2

Step-by-step explanation:

Use the slope formula when given two points

Slope formula = \frac{y_2-y_1}{x_2-x_1}

( the x and y values are determined by the given points )

Given the points ( 0 , 5 ) and ( 1 , 3 )

Plug in the x and y values of the given points into the formula

( remember y values on top x values on bottom )

slope=\frac{5-3}{0-1} \\5-3=2\\0-1=-1\\slope=\frac{2}{-1} =-2

Hence, the answer is D

5 0
3 years ago
Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longbo
Alisiya [41]

Answer:

Do not reject H0. The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders

Step-by-step explanation:

The null hypothesis is that  the mean days surfed for all long boarders is larger than the mean days surfed for all short boarders

H0:  μL > μs      against the claim Ha:  μL≤ μs

the alternate hypothesis is the mean days surfed for all long boarders isless or equal to  the mean days surfed for all short boarders (because long boards can go out in many different surfing conditions)

The test statistic is

t= x1- x2/  √s1/n1+ s2/n2

1) Calculations

Longboards

Mean

ˉx=∑x/n=4+8+9+4+9+7+9+6+6+11+15+13+16+12+10+12+18+20+15+10+15+19+21+9+22+19+23+13+12+10/30

=377/30

=12.5667

Longboard Variance S2=[∑dx²-(∑dx)²/n]/n-1

=[831-(-13)²/30]/29

=831-5.6333/29

=825.3667/29

=28.4609

Shortboard Mean

ˉx=∑x/n=6+4+6+6+7+7+7+10+4+6+7+5+8+9+4+15+13+9+12+11+12+13+9+11+13+15+9+19+20+11/30

=288/30

=9.6

Shortboard Variance S2=[∑x²-(∑x)²/n]/n-1

=[ 3270-(288)2/30]/29

=3270-2764.8/29

=505.2/29

=17.4207

2) Putting values in the test statistic

t=|x1-x2|/√S²1/n1+S²2/n2

t =|12.5667-9.6|/√28.4609/30+17.4207/30

t =|2.9667|/√0.9487+0.5807

t=|2.9667|/√1.5294

t=|2.9667|/1.2367

t=2.3989

3) Degree of freedom =n1+n2-2=30+30-2=58

4) The critical region is t ≤ t(0.05) (58) =1.6716

5) Since the calculated t= 2.4 does not fall in the critical region t(0.05) (58)  ≤ 1.6716 we do not reject H0.

The p-value is 0.008969. The result is significant at p <0 .05.

6 0
3 years ago
Solve the equation X=
4vir4ik [10]

Step-by-step explanation:

I think the answer is x=70

7 0
2 years ago
Other questions:
  • How many yards does 3 miles make
    9·2 answers
  • Jeremy washes 3/8 of the plates from dinner if 16 plates were used how many plates did Jeremy wash
    8·1 answer
  • The two squares in the graph below are similar. Which sequence of transformations proves that the squares are similar?
    5·1 answer
  • 17/19 is equal to what fraction A 80/95 B 43/57 C 50/57 D 85/95
    7·2 answers
  • Help me out tysm!! &lt;3 marking brainliest for the person who answers all correctly.
    13·2 answers
  • Pls help <br> Show workings
    9·1 answer
  • Find the percent markdown for an $120 shirt that is on sale for $90
    15·1 answer
  • By how much is 18 greater than -8​
    9·2 answers
  • Help I'm trying to do this but i cant
    10·1 answer
  • If w = 7 feet, x = 6 feet, y = 13 feet, and z = 8 feet, what is the area of the object?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!