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Andrews [41]
2 years ago
14

Which of the following rational functions is graphed below?

Mathematics
1 answer:
vichka [17]2 years ago
3 0

The answer is choice A

Hope it helps

Please give brainliest

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The graph of the function f(x) = (x +2)(x + 6) is shown
dalvyx [7]

The true about the domain and the range of the function is:

The domain is all real numbers, and the range is all real  numbers

greater than or equal to -4 ⇒ 1st answer

Step-by-step explanation:

f(x) = (x + 2)(x + 6) is a quadratic function with 2 factors (x + 2) and (x + 6)

By multiplying its two factors we will find the form of the quadratic function

∵ (x)(x) = x²

∵ (x)(6) = 6x

∵ (2)(x) = 2x

∵ (2)(6) = 12

∴ f(x) = x² + 6x + 2x + 12

- By adding like terms

∴ f(x) = x² + 8x + 12

The quadratic function represented graphically by a parabola

Look to the attached figure

The x-coordinate of the vertex point of the parabola h = \frac{-b}{a}

where b is the coefficient of x and a is the coefficient of x²

∵ f(x) = x² + 8x + 12

∴ a = 1 and b = 8

∴ h = \frac{-8}{2*1}=-4

The y-coordinate of the vertex point is k = f(h)

∵ h = -4

∴ k = f(-4)

∴ k = (-4)² + 8(-4) = 12 = 16 - 32 + 12

∴ k = -4

∴ The vertex point of the parabola is (-4 , -4)

∵ The parabola is opened upward

∴ Its vertex is minimum point

∴ The minimum value of f(x) is y = -4

∵ The domain of the function is the values of x

∵ The range of the function is the values of y corresponding to the

   values of x

∵ x can be any real numbers

∴ x ∈ R, where R is the set of real numbers

∴ The domain of f(x) is all real numbers

∵ The minimum value of f(x) is y = -4

∴ y can be any real number greater than or equal to -4

∴ y ≥ -4

∴ The range is all real number greater than or equal to -4

The true about the domain and the range of the function is:

The domain is all real numbers, and the range is all real  numbers

greater than or equal to -4

Learn more:

You can learn more about quadratic function in brainly.com/question/1332667

#LearnwithBrainly

7 0
2 years ago
What is the solution of the system of equations? -y+3x=6 y=-6x+12
irinina [24]

Answer:

x = 2

y = 0

Step-by-step explanation:

We can solve using substitution, substitute y in the first equation with the second equation:

-(-6x + 12) + 3x = 6

Distribute the negative sign:

6x - 12 + 3x = 6

Combine like terms:

9x - 12 = 6

Isolate the variable and solve for x by adding 12 in both sides:

9x = 18

x = 2

Substitute 2 with x in any equation to find the value of y:

-y + 3(2) = 6

-y + 6 = 6

Subtract 6 in both sides to isolate the variable:

-y = 0

0/-1 = 0

y = 0

Our answer would be x = 2 and y = 0

8 0
3 years ago
Read 2 more answers
Which situation is repesented by the graph
forsale [732]

Answer:

answer is A i think im not sure

Step-by-step explanation:

i dont know ask your teacher

4 0
3 years ago
Solve absolute value equation 2|x-3|-8=2
Semmy [17]

Answer:

x=8, -2

Step-by-step explanation:

2|x-3|-8=2

2|x-3|=10

|x-3|=5                               |x-3|=-5

x-3=5                                x-3=-5

x=8                                      x=-2

7 0
3 years ago
Tyree bought a collectible comic book for $49.62 last year. this year, he sold it for $52.10. find the percent of change of the
lidiya [134]
52.10-49.62=2.48
2.48/49.62 x 100 = 4.998%
The percentage increase in the price is approximately 5 %
3 0
3 years ago
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