Question 5

Question 5

Consider the function $g(x) = 2\sin^{–1}{(3x)}$.

Which transformations have been applied to $f(x) = \sin^{–1}(x)$ to obtain $g(x)$?

A. Vertical dilation by a factor of $\displaystyle \frac12$ and a horizontal dilation by a factor of $\displaystyle \frac13$

B. Vertical dilation by a factor of $\displaystyle \frac12$ and a horizontal dilation by a factor of $\displaystyle 3$

C. Vertical dilation by a factor of $\displaystyle 2$ and a horizontal dilation by a factor of $\displaystyle \frac13$

D. Vertical dilation by a factor of $\displaystyle 2$ and a horizontal dilation by a factor of $\displaystyle 3$

Solution

By multiplying the function by $2$, we double the range of $f(x)$ range and so dilate the graph vertically by a factor of $2$.

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