Question

The graph below shows two functions: function f of x is a straight line which joins the ordered pairs negative 2.5, 9 and 2.5, negative 1. Function g of x is a curved line which joins the ordered pairs negative 1.4, 6.8 and 2, 0.2 Based on the graph, what are the approximate solutions to the equation −2x + 4 = (0.25)x?

Answer 1

just took the test and this is the correct answer -1.4, 2.

Answer 2

We are looking for the approximate solution of
`-2x+4=(0.25)^x`, that is, we are looking for the solution of the equation f(x)=g(x).

The solution of this equation are represented by the intersecting points (x, y) of the graphs of these functions, because the intersecting points (x, y) are such that

y=f(x), but also y=g(x).


From the graph, we can see that there are two solutions, one is at approximately x=2, and the other is approximately -1.4.


Answer: -1.4, 2.