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marissa [1.9K]
2 years ago
14

Find the domain and range of f(x)= (2x+6) / ((x^2)-x-12)

Mathematics
1 answer:
creativ13 [48]2 years ago
8 0

Answer:

Step-by-step explanation:

If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away.  If there is, this affects the domain.  The domain are the values in the denominator that the function covers as far as the x-values go.  If we factor both the numerator and denominator, we get this:

f(x)=\frac{2(x+3)}{(x-4)(x+3)}

Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away.  That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x.  The other factor, (x - 4), does not cancel out.  This is called a vertical asymptote and affects the domain of the function.  Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4.  That means that the function has to split at that x-value.  It comes in from the left, from negative infinity and goes down to negative infinity at x = 4.  Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity.  The domain is:

(-∞, 4) U (4, ∞)

The range is (-∞, ∞)

If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.

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KatRina [158]

Answer:

B I think

Step-by-step explanation:

Eight eighths in one cup. Took that and multiplied that and added the single eighth. Six sixths in one cup. Took that and multiplied that and added the single sixth again. Added the total up and got 10.2916666667. Rounded. Hope this helps!

3 0
2 years ago
Read 2 more answers
1) A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hou
Ronch [10]

The mean ( average ) is given as 1200 hours.

The standard deviation is 200, sample size is 100.

Find the standard error:

√(200^2 / 100) = 20

Now calculate the confidence interval. For 95% the Z number is 1.96

Multiply Z by the standard error:

1.96 x 20 =39.2

Now find the range that the mean should be within:

1200 - 39.2 = 1160.8

1200 + 39.2 = 1239.2

The samples should be between 1160.8 and 1239.2 for a 95% confidence interval.

Since the average was 1050, which is below 1160.8 the bulbs are not in compliance.

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3 years ago
URGENT WILL GIVE BRAINLEIST
Rufina [12.5K]
What is it?? What’s the question
4 0
2 years ago
A company makes poppy lapel pins.
mezya [45]

Answer:

<h2>The required percentage is 65.45%.</h2>

Step-by-step explanation:

The total costing is 1000 \times 1.10 = 1100

35% were given to the charity, hence 350 were given to the charity.

There are (1000 - 350) = 650 lapel pins remaining.

60% of 650 = \frac{60}{100} \times 650 = 390 werre sold for 3.00 each. Hence, earning from here is 390 \times3 = 1170.

40% of 650 = 260 were sold at 5.00 for 2. It can also be said that \frac{260}{2} = 130 were sold at 5.00 each. Earning from this section is 130 \times5 = 650

Total earning is (1170 + 650) = 1820.

Profit percentage = \frac{1820 - 1100}{1100} \times100 = \frac{720}{11} = 65.45

5 0
3 years ago
Please help thank you​
nikdorinn [45]

Answer:

See explanation

Step-by-step explanation:

(x^2+9x+10)(x-2)= \\\\x^3-2x^2+9x^2-18x+10x-20= \\\\x^3+7x^2-8x-20

Jimmy is incorrect.

Using long division, you can find that the real answer.

First, subtract x^2(x-2) from the original expression, leaving you with 9x^2+2x-40.

Next, subtract 9x(x-2) from the expression, leaving you with 20x-40. Finally, subtract 20(x-2) from the expression, leaving you with a remainder of 0. This means that the real quotient is x^2+9x+20. Hope this helps!

6 0
3 years ago
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