Question

Write the equation of the function graphed below: x) =x√3x3– 4f(x) =x√3x3+ 4f(x) = 2x√3x3+ 4f(x) = 2x√3x3–4

Answer 1

The graph is showing the behaviour of the function x^1/2, then, let's start with it:

`f(x)=\sqrt[]{x}`

Now, we try to reach the given graph by multiplying and adding numbers to f(x). Firstly, the graph is always negative, so we multiply f(x) by -1.

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

Then, let's move the graph five units to the positive x position. To do so, we can add -5 to the x.

`h(x)=-\sqrt[]{x-5}`

Finally, we need to multiply the function so that the curve opens at the rate of the given graph.

`m(x)=-2\cdot\sqrt[]{x-5}`

As you can see, the graph is changing as we add or multiply by some factors. the red curve is pretty close to the given graph.