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How do you identify the zeros of a polynomial function?
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Zeros of a polynomial function are the values of x where f(x) = 0, such as x = -2, 0, 2 for the polynomial f(x) = x³ - 4x.
Compare the growth rates of exponential and polynomial functions.
Exponential functions grow faster than polynomial functions. For large values of x, exponential terms dominate polynomial terms.
How can you graphically recognize a logarithmic function?
A logarithmic function graph is the inverse of the exponential function graph and only exists for a positive base.
What is a tangent line and where does it touch a curve?
A tangent line is a line that touches a curve at a single point without crossing it, such as at the vertex of a parabola.
Explain the concept of a function's range.
The range of a function is the subset of the codomain which contains the values that the function actually takes.
What are the characteristics of a linear function's graph?
A linear function graph is a straight line where 'm' is the slope and 'c' is the y-intercept.
Provide the general form of a polynomial function.
The general form of a polynomial function is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_0.
Identify the minimum value location of a quadratic function in vertex form.
The minimum or maximum value of a quadratic function in vertex form f(x) = a(x-b)² + c occurs at x = b.
Explain how the vertex form of a quadratic function determines the direction a parabola opens.
The quadratic function f(x) = a(x-b)² + c forms a parabola. If 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.
Define a function and give an example of notation.
A function is a relation where each input from the domain corresponds to exactly one output in the codomain. For example, f: R -> R, where f(x) is a mapping from a subset of real numbers to real numbers.
How is a logarithmic function related to an exponential function?
A logarithmic function is the inverse of an exponential function, with base a > 0 corresponding inversely to the base of the exponential function.
What implications does the base of an exponential function have on its behavior?
The base of an exponential function must be positive (>0) to ensure the function is defined for all real numbers and maintains its growth traits.
What differentiates a quadratic function from a linear one?
A quadratic function involves the square of the variable, forming a parabola, whereas a linear function defines a straight line.
Describe an exponential function and its domain.
An exponential function is of the form f(x) = a^x with a > 0, and it is defined for all real numbers.
What characterizes a monotonic increasing function?
In a monotonic increasing function, if x1 ≤ x2 then f(x1) ≤ f(x2). The graph consistently ascends with increasing x.
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