Question

the function f(x) has the properties listed below. • lim┬(x→+∞)⁡〖f(x)〗 =∞ • lim┬(x→ -∞)⁡〖f(x)〗 = -∞ • f(x) does not have a vertical asymptote • f(x) does not have an inflection point which of the models weve learned could this function be? • periodic/sine • logarithmic • cubic • exponential • linear • quadratic • logistic clear my selection multiple choice 2 points

Explanation:

1. Linear function: A linear function \(y = mx + b\) has a constant slope and no vertical asymptotes and no inflection points. Its limit as \(x\to\pm\infty\) is either \(\infty\) or \(-\infty\) depending on the sign of \(m\).
2. Quadratic function: A quadratic function \(y=ax^{2}+bx + c\) (\(a

eq0\)) has an inflection - point at \(x =-\frac{b}{2a}\) when \(a
eq0\) and has no vertical asymptotes. Its limit as \(x\to\pm\infty\) is \(\pm\infty\) depending on the sign of \(a\).

1. Cubic function: A cubic function \(y = ax^{3}+bx^{2}+cx + d\) (\(a

eq0\)) has an inflection - point. Its limit as \(x\to\pm\infty\) is \(\pm\infty\) depending on the sign of \(a\).

1. Exponential function: An exponential function \(y = a\cdot b^{x}\) (\(b>0,b

eq1\)) has no inflection - points in the basic form. It has a horizontal asymptote (\(y = 0\) for \(|b|<1\) as \(x\to\infty\) or \(|b| > 1\) as \(x\to-\infty\)), not a vertical asymptote. Its limit as \(x\to\pm\infty\) is either \(\infty\) or \(0\) or \(-\infty\) depending on the values of \(a\) and \(b\).

1. Logarithmic function: A logarithmic function \(y=\log_{b}(x)\) (\(b > 0,b

eq1\)) has a vertical asymptote at \(x = 0\).

1. Logistic function: A logistic function \(y=\frac{L}{1 + e^{-k(x - x_{0})}}\) has a horizontal asymptote (\(y = 0\) and \(y = L\)) and an inflection - point at \(x=x_{0}\).
2. Periodic/sine function: A sine function \(y = A\sin(Bx - C)+D\) has no vertical asymptotes and has inflection - points.

A linear function does not have a vertical asymptote and does not have an inflection - point among the given properties.

Answer:

linear