Question

Select the graph of g(x)=3csc1/3x . Then describe the graph of g as a transformation of the graph of f(x)=cscx 

Answer 1

Given the parent function is $f(x)=cscx$

And the final transformation function is

$g(x)=3csc\frac{1}{3}x$

The graph of parent function is:

The graph of a function $h(x)=af(x)$ is the vertical stretch of the graph of (fx) if |a|>1

Let a=3

Hence the graph of a function $h(x)=af(x)=3csc(x)$ is the vertical stretch of the graph of $f(x)=CSC(x)$ .

The graph of function $h(x)=3csc(x)$ is:

The graph function $g(x)=h(bx)$ is the horizontal stretch of the graph of h(x) if 0<|b|<1

Let $b=\frac{1}{3}$

Hence the graph of a function $g(x)=h(\frac{1}{3}x)=3csc(\frac{1}{3}x)$ is the horizontal stretch of the graph of $h(x)=3csc(x)$ .

The graph of a function $g(x)=3csc(\frac{1}{3}x)$ is