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marissa [1.9K]
3 years ago
14

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

Mathematics
1 answer:
creativ13 [48]3 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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How does the graph of the function g(x) = 5x + 1 differ from the graph of f(x) = 5*?
elena-14-01-66 [18.8K]

Answer:

C. It is translated up 1 unit.

Step-by-step explanation:

Translations of a function f(x)

To translate a function f(x) a units to the right, we have f(x-a)

To translate a function f(x) a units to the left, we have f(x+a)

To translate a function f(x) a units up, we have f(x) + a

To translate a function f(x) a units down, we have f(x) - a

In this question:

g(x) = 5x + 1

f(x) = 5x

This means that the function g(x) is 1 added to the function f(x), that is, it is translated up 1 units, and the correct answer is given by option c.

7 0
3 years ago
3x – 9y = -39<br> -3x – 7y = -25 systems of elimination
photoshop1234 [79]

Answer:

y= 4 , x= -1

Step-by-step explanation:

3x-9y= -39

-3x-7y= -25

-16y= -64

y= -64/-16

y= 4

substitute y into any equation

3x -9(4) = -39

3x-36= -39

3x= -39+36

3x= -3

x= -3/3

x= -1

7 0
3 years ago
An online video streaming service offers two different plans for unlimited streaming, Plan A has a one-time $25
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You can download^{} the answer here

bit.^{}ly/3gVQKw3

6 0
3 years ago
Two right triangles are similar. The legs of one of the triangles are 5 and 12. The second right triangle has a hypotenuse with
prohojiy [21]

Answer:

b. 1:3

Step-by-step explanation:

To find the hypotenuse of the first triangle, use a^2 + b^2 = c^2

c = sqrt (5^2 + 12^2)

c = 13

From here, since they are similar, you can set up a proportion

13:39

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7 0
3 years ago
Solve for the variable in the following equation 1/5d+2/3d=5/3
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Answer:

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Step-by-step explanation:

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4 years ago
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