Question

Identify the functions in the graph and match the columns

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The graph of $x^{\frac{1}{2}}$ and $x^{\frac{1}{4}}$ will be similar. $\sqrt{x}$ and $x^{\frac{1}{4}}$ are not defined for x<0.

So these graphs will only be plotted for +ve values of x. Once we identify the two graphs we have to distinguish between $x^{\frac{1}{2}}$ and $x^{\frac{1}{4}}$. For that we can look at the interval[0,1]. $x^{\frac{1}{4}}$ is greater than $x^{\frac{1}{2}}$ in that interval.
For example,$(\frac{1}{16}{)}^{\frac{1}{4}}$ > $(\frac{1}{16}{)}^{\frac{1}{2}}$ because $\frac{1}{2}$ > $\frac{1}{4}$.
So the graph of $x^{\frac{1}{4}}$ will be alone $x^{\frac{1}{2}}$ in the interval (0,1).
The other two graphs will be of $x^{\frac{1}{3}}$ and $x^{\frac{1}{5}}$. We can distinguish between these two graphs the same way we did for $x^{\frac{1}{2}}$ and $x^{\frac{1}{4}}$.
The graph which lies above will be the graph will be the graph of $x^{\frac{1}{5}}$ in the interval (0,1).