Question

Let, `f(x)=-3/2x` and `g(x)=(1/2)^x-1`. `" "` What are the solutions to the equation `f(x)=g(x)`? `" "`Also graph the functions on the same coordinate plane!

Answer 1

`x = -2, x = 0`

Explanation:

the graph of `f(x) = -3/2x` can be drawn using two points.

this could be `(0,0)` and `(2, -3)` or `(0,0)` and `(-2, 3)`, for example.

the graph of `f(x) = -3/2x` is a straight line, with the same gradient throughout.

the graph of `g(x) = (1/2)^x - 1` can also be drawn using two reference points, e.g. `(0,0)` and `(-2, 3)`

however, it is important to note that it is a curve, and that its gradient decreases as `x` increases.

it is also important for the graph not to touch the line `y = -1`. the value of `y` only tends towards it as `x` nears infinity, since this is the value of `x` at which `(1/2)^x` would tend to `0`.

the coordinates at which these graphs meet are

`(-2, 3)`

and

`(0,0)`

and the `x`-values of these coordinates are `-2` and `0`.