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2 years ago

Which of the following does not represent an attribute of the function f(x) = [x]?

Mathematics

2 answers:

luda_lava [24]2 years ago

4 0

Answer: The graph has a line of symmetry at y = 0.

Step-by-step explanation:

I suppose that this refers to the function:

f(x) = IxI

The parent absolute value function.

Remember how this works:

IxI = x if x ≥ 0

IxI = -x if x ≤ 0.

Let's analyze the sentences:

1) "The x- and y-intercepts are (0,0)"

This is true, when x = 0 we have:

y = f(0) = I0I = 0

So the point (0, 0) is the only x-intercept and the only y-intercept.

2) "Domain: (-∞,∞); Range: [0,∞)"

This is also true, we clearly do not have any restriction in the domain.

And when looking at the range, we can see that the possible values of y are always positive or zero.

3) "(0, 0) is the minimum point."

Now, as x increases in the positive range, also does the value of y.

And as x decreases in the negative range, as the absolute value changes the sign, we will also have an increase in the value of y.

Then we have that (0, 0) must be the minimum.

4) "The graph has a line of symmetry at y = 0."

This is false.

The real line of symmetry is at x = 0, y = 0 corresponds to the x-axis, and as the graph opens up, we can not have symmetry about any line parallel to the x-axis.

ollegr [7]2 years ago

4 0

Answer:

Step-by-step explanation:

The graph has a line of symmetry at y = 0.

You might be interested in

What is the simplest form of RootIndex 3 StartRoot 27 a cubed b Superscript 7 Baseline EndRoot?

Vinvika [58]

Answer: $3ab\sqrt[3]{b^4}$

Step-by-step explanation:

Given the following expression:

$\sqrt[3]{27a^3b^7}$

You need to apply the Product of powers property, which states that:

$(a^m)(a^n)=a^{(m+n)$

Then, you can rewrite the expression as following:

$=\sqrt[3]{27a^3b^4b^3}$

The next step is to descompose 27 into its prime factors:

$27=3*3*3=3^3$

Now you must substitute $3^3$ inside the given root. Then:

$=\sqrt[3]{3^3a^3b^4b^3}$

You need to remember that, according to Radicals properties:

$\sqrt[n]{a^n}=a^{\frac{n}{n}}=a^1=a$

Therefore, the final step is to apply this property in order to finally get the expression is its simplest form. This is:

$=3^{\frac{3}{3}}a^{\frac{3}{3}}b^{\frac{4}{3}}b^{\frac{3}{3}}=3ab^{\frac{4}{3}}b=3ab\sqrt[3]{b^4}$

3 0

2 years ago

Read 2 more answers

ratelena [41]

Answer:

The no. of possible handshakes takes place are 45.

Step-by-step explanation:

Given : There are 10 people in the party .

To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?

Solution:

We are given that there are 10 people in the party

No. of people involved in one handshake = 2

To find the no. of possible handshakes between 10 people we will use combination over here

Formula : $^nC_r=\frac{n!}{r!(n-r)!}$

n = 10

r= 2

Substitute the values in the formula

$^{10}C_{2}=\frac{10!}{2!(10-2)!}$

$^{10}C_{2}=\frac{10!}{2!(8)!}$

$^{10}C_{2}=\frac{10 \times 9 \times 8!}{2!(8)!}$

$^{10}C_{2}=\frac{10 \times 9 }{2 \times 1}$

$^{10}C_{2}=45$

No. of possible handshakes are 45

Hence The no. of possible handshakes takes place are 45.

4 0

2 years ago

Which expressions are equivalent to -6n+(-12)+4n

GaryK [48]

Answer:

-2n - 12

Step-by-step explanation:

Combine like terms. Note that each term has one variable (n). Also note that one negative sign and one positive sign results in a negative sign.

-6n + (-12) + 4n = -6n + 4n - 12 = -2n - 12

-2n - 12 is your answer

5 0

2 years ago

RANDOMLY CHOOSING TWO POTENTIAL CLIENTS

gregori [183]

Let Jacob, Carol, Geraldo, Meg, Earvin, Dora, Adam, and Sally be represented by the letters J, C, G, M, E, D, A, and S respectively. 

In part IV we are asked:

What is the sample space of the pairs of potential clients that could be chosen?

Since the Sample Space is the set of all possible outcomes, we need to make a set (a list) of all the possible pairs, which are as follows:

{(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S)

, (C, G), (C, M), (C, E), (C, D), (C, A), (C, S)

 , (G, M), (G, E), (G, D), (G, A), (G, S)

 ,(M, E), (M, D), (M, A), (M, S)

, (E, D), (E, A), (E, S) 

, (D, A), (D, S)

, (A, S).}

We can check that the number of the elements of the sample space, n(S) is

1+2+3+4+5+6+7=28.

This gives us the answer to the first question: How many pairs of potential clients can be randomly chosen from the pool of eight candidates?

(Answer: 28.)

II) What is the probability of any particular pair being chosen?

The probability of a particular pair to be picked is 1/28, as there is only one way of choosing a particular pair, out of 28 possible pairs.

III) What is the probability that the pair chosen is Jacob and Meg or Geraldo and Sally?

The probability of choosing (J, M) or (G, S) is 2 out of 28, that is 1/14.

Answers:

I) 28
II) 1/28≈0.0357
III) 1/14≈0.0714
IV)

{(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S)
, (C, G), (C, M), (C, E), (C, D), (C, A), (C, S)
, (G, M), (G, E), (G, D), (G, A), (G, S)
,(M, E), (M, D), (M, A), (M, S)
, (E, D), (E, A), (E, S)
 , (D, A), (D, S)
, (A, S).}

6 0

2 years ago

Darius is a broker who earns a $68,000 annual salary, a 3.15% commission on his clients’ investments, and a fee of $4.25 for eac

taurus [48]

Answer:

$187,244

Step-by-step explanation:

$68,000 annual salary + 3.15% commission + fee of $4.25 per transaction

$68,000 + 0.0315 * $3,600,000 + $4.25 * 1,375 =

= $187,243.75

Answer: $187,244

4 0

2 years ago