Part 3

Geometry Level 3

Which of the following graph correctly represents $\large{x^{\frac{7}{3} }}$ .

A)
B)
C)
D) None of them

Also try Part 1 and Part 2

B A C D

2 solutions

Akhil Bansal
Aug 30, 2015

Actual graph is

This is because we note that the denominator of $x^{\frac{7}{3}}$ is odd, which means the function is defined for all $x\in\mathbb{R}$ , not just $x\in\mathbb{R}^+$

Daniel Liu - 5 years, 9 months ago

Blan Morrison
Oct 25, 2018

If we take the cube root of a negative number, then the cube root will remain real. Therefore, we can eliminate A and C. We can eliminate B because $\displaystyle\lim_{x\rightarrow \infty} B'(x)=0$ (meaning the graph's rate of change gets smaller and smaller); in $x^{\frac{7}{3}}$ , this is not the case. Therefore, the answer is D. $~\beta_{\lceil \mid \rceil}$

Part 3

2 solutions

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