Question 1
The function \(f\) is defined by \(f(x) = 2x^2 - 12x + 22\). The graph of \(f\) in the \(xy\)-plane is a parabola. What is the minimum value of \(f(x)\)?
Hard - Quiz 1
Work through challenging problems involving transformations, composed functions, and advanced behavior of quadratic, exponential, and rational models.
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A biologist models two competing bacteria populations with the functions \(A(t) = 800 \cdot (1.5)^t\) and \(B(t) = 200 \cdot (3)^t\), where \(t\) is time in days. After how many days will the two populations be equal?
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The function \(g\) is defined by \(g(x) = \dfrac{2x + 6}{x - 1}\). Which of the following is an equivalent form that reveals the horizontal asymptote of \(g\)?
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Let \(f(x) = x^2 + 1\) and \(g(x) = 3x - 2\). What is the value of \(f(g(3))\)?
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A town's annual revenue \(R\), in thousands of dollars, is modeled by \(R(t) = -4t^2 + 48t + 100\), where \(t\) is the number of years after 2020. According to the model, in what year does the town reach its maximum revenue?