Question

Can you help me figure out the equation in the drop down menus

Answer 1

To find:

The piecewise function for the graph.

Solution:

From the graph, it is clear that when x is less than -1, the graph passes through (-1, -3) and (-2, -5).

It is known that the equation of a line passes through two points is given by:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

So, the equation of line passing through (-1, -3) and (-2, -5) is:

`\begin{gathered} y-(-3)=(-5-(-3))/(-2-(-1))(x-(-1)) \\ y+3=(-2)/(-1)(x+1) \\ y+3=2x+2 \\ y=2x-1 \end{gathered}`

So, the first drop down is "2x - 1", and second drop down is "x is less than or equal to -1".

Now, the graph passes through (1, 5) and (2, 6). So, the equation of the line is:

`\begin{gathered} y-5=(6-5)/(2-1)(x-1) \\ y-5=x-1 \\ y=x+4 \end{gathered}`

So, the third drop down menu is "x + 4" and the fourth drop down menu is "x is greater than or equal to 1".