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3 years ago

Which statement is true about the function

Mathematics

2 answers:

Vikentia [17]3 years ago

6 0

Answer:

Option A is the answer.

Step-by-step explanation:

Given function is f(x) = - $\sqrt{-x}$

Option A. Domain of the function is all negative real numbers.

As we know under root of any negative number is not defined so this function is defined only for the values of x ≤ 0

Example : f(1) = -√(-1) Not defined

and f(-1) = -√-(-1) = √1 Defined

Therefore, domain of the function will be all negative real numbers.

Option B. Range of the function is all positive real numbers.

Example: f(-1) = -√-(-1) = -√1

= - 1

For x = -1, range of the function is negative.

Therefore, this option is not true.

Option C. Domain and Range of the function have opposite signs.

As we have seen in option B.

f(-1) = - 1

Therefore, domain and range of the function are of same sign. So this option is incorrect.

Option D. Domain and range of the function are same.

Example: f(-2) = -√-(-2) = -√2

= - 1.414 ≠ (-2)

Therefore, Domain and range are not same which shows that this option is incorrect.

Option A will be the answer.

Lana71 [14]3 years ago

4 0

You solve for the domain by setting the radicand less than or equal to 0 and solving for x. Dividing by a -x, we switch the sign so we have that the domain is less than or equal to 0, or all negative numbers. We know that it breaks every law in math to have a negative radicand with an even index, so if the domain is all negative values of x, taking a negative of a negative gives us a positive. The negative sign OUTSIDE the radical means you are flipping the graph upside down. So instead of having a range of y is greater than or equal to 0 as does the parent graph, you have flipped it upside down so it heads more negative in regards to the range. Therefore, the domain and the range both have the same sign, thee last choice from above.

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A two-digit number becomes 5/6 of the reversed number obtained when the digits are interchanged. The difference between the digi

stealth61 [152]

<h3>Answer: 54</h3>

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

Work Shown:

T = tens digit

U = units digit (aka ones digit)

A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).

-----------------------

Let T be larger than U. This doesn't work if T = U.

Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.

-----------------------

If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.

So,

new number = (5/6)*(old number)

10U + T = (5/6)(10T + U)

6(10U + T) = 5(10T + U)

60U + 6T = 50T + 5U

60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1

60U + 6U + 6 = 50U + 50 + 5U

66U + 6 = 55U + 50

66U - 55U = 50-6

11U = 44

U = 44/11

U = 4 is the units digit of the original number

T = U+1

T = 4+1

T = 5 is the tens digit of the original number

The original number is therefore 10T + U = 10*5+4 = 54.

We see the difference in their digits is T-U = 5-4 = 1

The reverse of 54 is 45. The number 45 is 5/6 of 54

45 = (5/6)*54

7 0

3 years ago

What is the answer to <br> 1+38*225(12/77)

Neporo4naja [7]

1+38*225(12/77)
1+38*225*6.41
1*8550*6.41
1+54,805.5
54,806.5
Use pemdas to solve it

4 0

3 years ago

Read 2 more answers

Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1

o-na [289]

Answer:

The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 <u><em>Expresion A</em></u>

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
If p> 0 and q <0, the parabola shifts p units to the right and q units down.
If p <0 and q> 0, the parabola shifts p units to the left and q units up.
If p <0 and q <0, the parabola shifts p units to the left and q units down.

In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, <u><em>the parabola is translated down 2 units.</em></u>

3 0

3 years ago

Terrence gets a loan with a $50 processing fee. The loan is for $700 with an interest rate of 8% for one

agasfer [191]

Answer:

15.14%

Step-by-step explanation:

The formula for APR is stated thus:

APR=fees+interest/principal/n*365*100

principal is the loan amount of $700

fees is the processing fees on the loan which is $50

interest amount=principal*interest %=$700*8%=$56

n is the number of days of the loan which is a year i.e 365 days

APR=($50+$56)/$700/365*365*100

APR=$106/$700/365*365*100

APR=0.151428571 /365*365*100

APR=0.151428571 *100=15.14%

The annual percentage rate on the loan is 15.14% which represents the actual cost on the loan not just the interest cost of 8% annually

4 0

3 years ago

Let U = {all integers}.

elixir [45]

All integer numbers are either even or odd. So, the complement to the set B (to the set of all even integers) is the set of all odd integers, that is D.

The integer number of the form 2x is always even, because it is always divided by 2, so the set C is the empty set.

Numbers 1, 3, 5, 7 are odd, therefore they belong to the set D.

7 0

3 years ago

Read 2 more answers