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Trava [24]
2 years ago
7

PLEASE HELP 20 points

Mathematics
1 answer:
Alona [7]2 years ago
7 0
1.
A-gp^49^6

2.
C-20x^4y^5
This is absolutely correct ^^^
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Consider the functions f(x) = 3x2, g(x)=1/3x , and h(x) = 3x. Which statements accurately compare the domain and range of the fu
Genrish500 [490]

Answer:

all of the functions have a unique range ⇒ answer 1

Step-by-step explanation:

* Lets revise how to find the domain and the range of the function

- The domain is all values of x that make the function defined

- The range is the set of all output values of a function

∵ f(x) = 3x²

- It is a quadratic function

- There is no values of x make this function undefined

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

- To find the range calculate the vertex of the function

∵ f(x) = ax² + bx + c

∵ f(x) = 3x²

∴ a = 3 , b = 0 , c = 0

∵ h = -b/2a

∴ h = 0/2(3) = 0/6 = 0

∵ k = f(h)

∴ k = f(0) = 3(0)² = 0

∴ The vertex of the cure is (0 , 0)

∵ k is the minimum value of the parabola

∴ The range of f(x) is all real numbers greater than or equal

  to zero ⇒ (1)

∵ g(x) = 1/3x

- It is a rational function

- to find the values of x which make the function undefined equate

 the denominator by 0

∵ 3x = 0 ⇒ divide both sides by 0

∴ x = 0

∴ The domain of g(x) is all real numbers except zero

∵ We can not put x = 0, then there is no value of g(x) at x = 0

∴ The range of the g(x) is all real number except zero ⇒ (2)

∵ h(x) = 3x

- It is a linear function

∵ There is no values of x make this function undefined

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

∴ The range of h(x) is all real numbers ⇒ (3)

* From (1) , (2) , (3) the answer is

 all of the functions have a unique range

# Look to the attached graph to more understand

The red graph is f(x)

The blue graph is g(x)

The green graph is h(x)

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