Question

Describe the transformations of the parent function to graph ( in picture). List at least 5 points that could be used to graph this function accurately without the use of a calculator

Answer 1

Notice that the parent function of f(x) is:

$g(x)=\sqrt[3]{x}.$

Now, to determine the transformations, we recall the following:

The graph of a function h(x)

1.- horizontally translated n units to the left is represented by the following function:

$l(x)=h(x+n),$

2.- vertically translated down m units:

$l(x)=h(x)-m,$

3.- reflected over the x-axis:

$l(x)=-h(x).$

Therefore, f(x) is g(x) translated 2 units to the left, reflected over the x-axis, and translated 4 units down.

To determine 5 points on the graph, we evaluate the graph at x=-2, x=6, x=-10, x=-1, x=-3, and get:

$\begin{gathered} f(-2)=-4, \\ f(6)=-2-4=-6, \\ f(-3)=1-4=-3, \\ f(-10)=2-4=-2, \\ f(-1)=-1-4=-5. \end{gathered}$

Therefore, the points (-2,-4),(6,-6),(-3,-3),(-10,-2),(-1,-5) are on the graph.

Answer:

f(x) is

$g(x)=\sqrt[3]{x}$

translated 2 units to the left, reflected over the x-axis, and translated 4 units down.

5 points on the graph:

(-2,-4),(6,-6),(-3,-3),(-10,-2),(-1,-5).