which of the following functions would have a graph with a horizontal s - shape? function #1: $y = \\tan x$…

which of the following functions would have a graph with a horizontal s - shape? function #1: $y = \\tan x$ function #2: $y = x^{3}$ function #3: $y = \\sqrt3{x}$ (1 point)

which of the following functions would have a graph with a horizontal s - shape? function #1: $y = \\tan x$ function #2: $y = x^{3}$ function #3: $y = \\sqrt3{x}$ (1 point)

Answer

Answer:

Function #2: $y = x^{3}$

Explanation:

Step1: Recall function shapes

The graph of $y=\tan x$ has vertical asymptotes and repeating U - shaped curves.

Step2: Analyze $y = x^{3}$

The cubic function $y = x^{3}$ has a horizontal S - shape. It passes through the origin $(0,0)$ and has a single inflection point at $x = 0$.

Step3: Analyze $y=\sqrt[3]{x}$

The graph of $y=\sqrt[3]{x}$ is also a cubic - like curve but has a different orientation and is not in a horizontal S - shape. It has a vertical tangent at $x = 0$.