Math 3 EOC review 2a

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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What does the function h(x) = 125x represent?

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The function h(x) = 125x models the total cost to purchase x sneakers, where each sneaker costs $125 before tax.

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What is the value of k in the function m(x) = kx after applying a 30% discount?

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The value of k is 87.5, representing the cost of x sneakers after a 30% discount.

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How do you find the inverse of a function?

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To find the inverse of a function, swap the x and y variables and solve for y. The inverse function undoes the action of the original function.

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What is the inverse of the function f(x) = 5⋅2^(3x)?

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The inverse is f^(-1)(x) = (log(x) - log(6)) / (2 * log(3)).

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Which type of function has an inverse that is also a function?

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A function must be one-to-one (bijective) to have an inverse that is also a function. For example, f(x) = (x-5)/3 is one-to-one.

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What is the significance of the logarithm in solving exponential equations?

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Logarithms are used to solve exponential equations by allowing us to bring the exponent down, making it easier to isolate the variable.

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What is the relationship between exponential and logarithmic functions?

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Exponential functions and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y).

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