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Questions and Answers
Which of the following equations best represents the quadratic function based on the provided values of x and f(x)?
Which of the following equations best represents the quadratic function based on the provided values of x and f(x)?
- f(x) = x^2 + 3
- f(x) = -x^2 + 3 (correct)
- f(x) = -2x^2
- f(x) = -2x^2 - 3
Which function listed is an odd function?
Which function listed is an odd function?
- f(x) = x^3 + x (correct)
- f(x) = -x^4 + x^2 - 1
- f(x) = 2x^3 + x - 2
- f(x) = 2x^4 + 6x^2 - 4x
What is the domain of the function $f(x) = \frac{3x - 1}{7}$?
What is the domain of the function $f(x) = \frac{3x - 1}{7}$?
- x < 1/3
- x > 1/3
- All real numbers (correct)
- x >= 1/3
What is the value of f(g(-1)) + g(f(1)) given the functions f(x) = x^2 and g(x) = 4 - 2x?
What is the value of f(g(-1)) + g(f(1)) given the functions f(x) = x^2 and g(x) = 4 - 2x?
What are the domain and range of the function $f(x) = \sqrt{16 - x^2}$?
What are the domain and range of the function $f(x) = \sqrt{16 - x^2}$?
What is the result of the composition (f ∘ g)(x) if f(x) = x + 1 and g(x) = \frac{x - 1}{x + 1}?
What is the result of the composition (f ∘ g)(x) if f(x) = x + 1 and g(x) = \frac{x - 1}{x + 1}?
What is the inverse of the function $f(x) = \frac{3x + 7}{7}$?
What is the inverse of the function $f(x) = \frac{3x + 7}{7}$?
Which of the following functions does NOT contain a maximum value?
Which of the following functions does NOT contain a maximum value?
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Study Notes
Quadratic Functions
- A quadratic function is a polynomial function of degree two.
- The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠0.
- The graph of a quadratic function is a parabola.
- The vertex of the parabola is the point where the function reaches its maximum or minimum value.
Odd and Even Functions
- A function f(x) is an odd function if f(-x) = -f(x) for all x in the domain.
- A function f(x) is an even function if f(-x) = f(x) for all x in the domain.
Domain and Range
- The domain of a function is the set of all possible input values (x-values).
- The range of a function is the set of all possible output values (y-values).
Function Composition
- The composition of two functions f(x) and g(x) is denoted by (f∘g)(x) and is defined as f(g(x))
- The composition of functions is a way of combining two functions to create a new function.
Inverse Functions
- The inverse of a function f(x) is denoted by f^-1(x) and is defined as the function that "undoes" the effect of f(x).
- The inverse of a function only exists if the function is one-to-one, which means that each input value has a unique output value.
- To find the inverse of a function, switch the x and y variables and then solve for y.
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