Question

For the graph `y=2^x/2` how we we get the (extra) coordinates (2,2)?

Answer 1

See the explanation

Explanation:

Note that `color(black)(2xx2^x=2^(x+1)` so `2^x -:2 = 2^(x-1)`

We can write `2^x` as `2xx2^(x-1)`

`color(green)(y=2^x /2 -> y=(2xx2^(x-1))/2)`

`color(green)(color(white)("ddddddddd") y=(cancel(2)xx2^(x-1))/cancel(2))`

Substitute `color(red)(2)` for `y`

`color(green)(color(red)(y)=2^(x-1)->color(red)(2)=2^(x-1)`

We know that `2=2` so this has to mean that

`color(green)(2=2^(x-1)->2=2)`

We also know that `2^1=2` so this has to mean that

`x-1=1`

Thus `x=2`

So the point `P_1->(x,y)=(2,2)` lies on the line `y=2^x /2`

Answer 2

Suppose you meant `y=2^(x/2)`

Explanation:

Set the point being investigated as `P_1->(x,y)=(2,2)`

By example note that `a^1=a; b^1=b; 3^1=3` and so on

Given that we are looking at `P_1->y=2` then we have:

Write as `y=2^1=2^(x/2)`

Then `x/2=1`

Multiply both sides by 2 and we have

`x=2`

So `y=2^(2/2) = 2`