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12345 [234]
3 years ago
14

The graph shows a vertical translation of y =

qrt[3]{x}" alt="\sqrt[3]{x}" align="absmiddle" class="latex-formula">
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}

Mathematics
1 answer:
Lisa [10]3 years ago
7 0

Answer:

  • Last option: {y|y is a real number}

Explanation:

The <em>range</em> of a real function is the set of the real numbers (values) that the function can return (the ouput of the function).

To figure out the range of a function, you first must figure out the domain.

The domain of the function   y=\sqrt[3]{x}  is all real values, since the cube root function is defined for all the real numbers.

Since this function is continuous (which the translation of the function shows graphically), and the function is defined for all negative and positive values, the range of   y=\sqrt[3]{x}  is all real numbers.

A vertical translation just slides the function vertically. Since the original function does not have either lower or upper bound, but the limits when x approaches ± ∞ are ± ∞, a translation will not modifiy the range.

Thus, <em>the range of the translated function</em> is (-∞, ∞).

That can also be written as <em>{y|y is a real number}</em>, which is read "y such that y is a real number", and is the last choice of the list.

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A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?
N76 [4]
If the series is made up of numbers in an arithmetic progression, you have

\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185

where a_1 is the first term and d is the common difference between terms.

Since the last term in the series is a_{18}=275, you have

a_{18}=a_1+(18-1)d\implies a_1+17d=275

Solve the system

\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}

and you'll find that the first term is a_1=190 (with d=5).
5 0
3 years ago
Raul has been offered three different jobs and must choose which one to accept. One of the factors he is considering is the pay
chubhunter [2.5K]

Answer:

As the pay rate for Job C is the highest, so he must accept the offer from Job C.

Step-by-step explanation:

Given that Raul would work 50 weeks of the year,

40 hours each week,

5 days each week,

and he would receive a 1-hour lunch break each day.

Pay rate for Job A = $35,000 / year

  • For Job B:

Pay rate = $15 / hour

He will work 40 hours each week.

As he works 5 days a week, so in 1 day he will work 40/5 = 8 hours.

He would receive a 1-hour break each day, for which he will not be paid, so he will receive a payment for 8-1=7 hours.

So, payment for 1 day = $15 x 7 = $105

As he works 5 days a week, so payment for 1 week = $105 x 5 = $525

As he works 50 weeks a year, so payment for 1 year = $525 x 50 = $26250.

So, the pay rate by Job B = $26250 /year

  • For Job C:

Pay rate = $750 / week

As he works 50 weeks a year, so payment for 1 year = $750 x 50 = $37500.

So, the pay rate by Job C = $37500 /year

As the pay rate for Job C is the highest, so he must accept the offer from Job C.

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3 years ago
Adam bought A new pair of baseball cleats for $65 the sales tax is 5.5% what is the total cost in dollars that Adam will pay
Dmitry [639]
(65×5.5%)+65 = 68.575
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3 years ago
Which graph equals ƒ(x) = -x + 6?
KIM [24]
The last graph is the answer
6 0
3 years ago
Read 2 more answers
Kiera is in her last year of college at the University of Houston. She has a scholarship that pays 75% of her costs. Her classes
sergiy2304 [10]
If the scholarship pays 75% of her classes cost, that means that she has to pay the 25% remaining of the classes cost so if we calculate it as follow:

0.25 * $14,000 = $3,500 
 =================================================================
Another method to understand:
if the scolarship pays 75% of her classes that will be 
0.75* $14,000 = $10,500

now she has to pay the remaining of the total cost and that will be 
$14,000 - $10,500 = $3,500.

5 0
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