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
nctions? Select two options.
1All of the functions have a unique range.
2The range of all three functions is all real numbers.
3 The domain of all three functions is all real numbers.
4The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.
5 The domain of f(x) and h(x) is all real numbers, but the domain of g(x) is all real numbers except 0.
1All of the functions have a unique range.
2The range of all three functions is all real numbers.
3 The domain of all three functions is all real numbers.
4The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.
5 The domain of f(x) and h(x) is all real numbers, but the domain of g(x) is all real numbers except 0.
2 answers:
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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