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2 years ago

Given 3x^2+x-4/x-1 what are the domain and range

Mathematics

1 answer:

Katarina [22]2 years ago

6 0

Answer:

doman: x ≠ 1
range: y ≠ 7

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

<h3>Simplified</h3>

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

$\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1$

<h3>Domain</h3>

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

x ≠ 1

In interval notation, this is ...

(-∞, 1) ∪ (1, ∞)

<h3>Range</h3>

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

y ≠ 7

In interval notation, this is ...

(-∞, 7) ∪ (7, ∞)

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Colin borrowed some money at 7.16%/a compounded quarterly. Three years later, he paid $5000 toward the principal and the interes

attashe74 [19]

Based on the calculations below, the amount originally borrowed by Colin is $10,006.67.

<h3>How do we calculate the original amount using PV formula?</h3>

To solve this question, the following present value (PV) formula will be used:

PVn = Pn / (1 + r)^n ........................... (1)

Where:

PVn = Present value of an amount paid in year n

P = Amount paid in year n

r = quarterly interest rate = 7.16% / Number of quarters in a year = 0.0716 / 4 = 0.0179

n = number of quarters = Number of years * Number of quarters in a year = Number of years * 4

Using equation (1), we can therefore proceed as follows:

PV3 = PV of $5,000 paid after three years = $5,000 / (1 + 0.0179)^(3 * 4) = $4,041.18

PV5 = PV of $5,000 paid after another 2 years (after 3 years + 2 years = 5) = $5,000 / (1 + 0.0179)^(5 * 4) = $3,506.45

PV10 = PV of $5,000 paid after another 5 years (after 3 years + 2 years + 5 years = 10) = $5,000 / (1 + 0.0179)^(10 * 4) = $2,459.04

Therefore, we have:

Original amount borrowed = PV3 + PV5 + PV10 = $4,041.18 + $3,506.45 + $2,459.04 = $10,006.67

Learn more about borrowing here: brainly.com/question/4239348.

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2 years ago

Complete the square.<br> x2 + 6x +<br> -<br> -<br> -

Shalnov [3]

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6 0

4 years ago

What is the y-coordinate for the solution of the system of equations below? 7y+5x=19 3y+5x=7

RoseWind [281]

I would go about solving this by elimination because the x variables are already the same so all you would have to do is change one equation to the opposite signs and add them, so it would look like:

7y + 5x = 19
+ -3y - 5x = -7
-------------------
4y=12
y=3

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3 years ago

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The radius of a circle is 6 yards. What is the circle's circumference? Use 3.14 for .

Orlov [11]

Answer:

18.84

Step-by-step explanation:

sorry if i get the wrong answer i literlly learn this but i complety forget it

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3 years ago

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Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week

antiseptic1488 [7]

Part A: W=6x
Part B: S=6(40)+9y
Part C: 330=6(40)+9y... 6(40)=240... 330-240=90...

9y=90... 9y/9= y... 90/9=10, therefore y=10

Andrew worked 40 regular hours and 10 overtime hours.

8 0

3 years ago