Question

3 multiple choice 2 points the function f(x) has the properties listed below: • lim_{x→∞} f(x)=-∞ • f(x) has an inflection point which of the models weve learned could this function be? logarithmic exponential linear cubic logistic periodic/sine quadratic clear my selection

Explanation:

Step1: Analyze logarithmic functions

Logarithmic functions like $y = \ln(x)$ have a vertical - asymptote and do not have inflection points in their domain. Also, $\lim_{x
ightarrow\infty}\ln(x)=\infty$, so it's not a logarithmic function.

Step2: Analyze exponential functions

Exponential functions $y = a^x$ ($a>0,a
eq1$) either increase or decrease without bound as $x
ightarrow\infty$ or $x
ightarrow-\infty$ and do not have inflection points (for basic exponential functions), so it's not an exponential function.

Step3: Analyze linear functions

Linear functions $y=mx + b$ are straight - lines, have no inflection points, so it's not a linear function.

Step4: Analyze cubic functions

Cubic functions $y = ax^3+bx^2+cx + d$ ($a
eq0$) can have inflection points. Also, if $a<0$, $\lim_{x
ightarrow\infty}ax^3+bx^2+cx + d=-\infty$. So a cubic function can satisfy the given properties.

Step5: Analyze logistic functions

Logistic functions $y=\frac{L}{1 + ae^{-bx}}$ have a horizontal asymptote, are S - shaped, and do not approach $-\infty$ as $x
ightarrow\infty$, so it's not a logistic function.

Step6: Analyze periodic/sine functions

Periodic/sine functions like $y = A\sin(Bx - C)+D$ are bounded functions and do not approach $-\infty$ as $x
ightarrow\infty$, so it's not a periodic/sine function.

Step7: Analyze quadratic functions

Quadratic functions $y = ax^2+bx + c$ ($a
eq0$) are parabolas, have a single vertex (not an inflection point in the non - degenerate sense), so it's not a quadratic function.

Answer:

cubic