Answer
Matching:
(a) -> (vi)
(b) -> (iv)
(c) -> (iii)
(d) -> (v)
(e) -> (i)
(f) -> (ii)
Work Step by Step
Reasons:
(a) -> (vi)
Similar shaped graphs for all odd numbers n, where $y = \sqrt[n] x$. Check graph of $y = \sqrt[3] x$. Hence, similar graph for $\sqrt[5] x$.
(b) -> (iv)
Same reasoning as above. The base graph remains similar to the graph of $y = x^{3}$. Multiplying with 2 and raising x to the fifth power does not change the shape much.
(c) -> (iii)
As x goes nearer and nearer to 0, the value of $-y$ becomes larger and larger. In this graph, you can clearly see -y getting very large when x approaches 0 from both left and right sides.
(d) -> (v)
The graph does not have values defined for all x, where $x^{2} < 1$. This is the gap you see in teh graph. When $x^{2} < 1$, the squre root is not defined because $x^{2} - 1$ becomes negative. Moreover, the graph is symmetric for both positive and negative values of x, because $x^{2}$ changes both positive and negative values to only positive.
(e) -> (i)
Similar graph to $y = \sqrt x$. The -2 simply shifts the starting point of the graph to (2,0). The shape approximately remains the same.
(f) -> (ii)
Both positive and negative values of x become positive because of $x^2$. The fifth root simply penalises x for being large. Large x's become smaller. This is why the graph does not rise as quickly as y = $x^2$. The negative sign just inverts the graph.
