Question

multiple choice 2 points 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

Explanation:

Step1: Recall function - property relationships

Linear functions are of the form $y = mx + b$. They have a constant slope and no vertical asymptotes, no inflection points, and $\lim_{x
ightarrow\pm\infty}f(x)=\pm\infty$ depending on the sign of $m$.

Step2: Analyze quadratic functions

Quadratic functions $y = ax^{2}+bx + c$ ($a
eq0$) have a single inflection - point (the vertex when $a
eq0$).

Step3: Analyze cubic functions

Cubic functions $y=ax^{3}+bx^{2}+cx + d$ ($a
eq0$) have an inflection point.

Step4: Analyze exponential functions

Exponential functions $y = a\cdot b^{x}+k$ ($b>0,b
eq1$) have horizontal asymptotes, no vertical asymptotes (in the basic form), and no inflection points in the simple cases.

Step5: Analyze logarithmic functions

Logarithmic functions $y=\log_{b}(x - h)+k$ have a vertical asymptote at $x = h$.

Step6: Analyze logistic functions

Logistic functions $y=\frac{L}{1 + ae^{-bx}}$ have horizontal asymptotes and no vertical asymptotes in the basic form.

Step7: Analyze periodic/sine functions

Sine - type functions $y = A\sin(Bx - C)+D$ are periodic, have no vertical asymptotes, and no inflection points in the simple cases.

A linear function $y = mx + b$ does not have a vertical asymptote and does not have an inflection point.

Answer:

linear