Question

The graph shows the function f(x) which equation represents f(x)

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

The parent cube root function is

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

From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.

If the parent cube root function is reflected across the y-axis, then x is replaced by -x.

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

Now, the graph of new function sifts 1 unit down. So, the required function is

$f(x)=\sqrt[3]{-x}-1$

The graph shows the function $f(x)=\sqrt[3]{-x}-1$.

From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).

Check the above function by these points.

At x=-8,

$f(-8)=\sqrt[3]{-(-8)}-1=2-1=1$

At x=0,

$f(0)=\sqrt[3]{-(0)}-1=0-1=-1$

At x=8,

$f(8)=\sqrt[3]{-(8)}-1=-2-1=-3$

All these points satisfy by the abobe function. It means the above function is correct.

Therefore the correct option is 3.

Answer 2

Try to find points with integer coordinates like (0, -1). Then substitute x in the equations and check which ones give the correct y. For my example, you substitute x by 0 and check if y is equal to -1. You find that only the third one holds true.