Question

What are the constants "a" and "b"?

Find the constants a and b such that the function is continuous.

Answer 1

`a=-1`
`b=1`

Explanation:

Since `f(x)=2` when `x<=-1`, all `y` values will be `2` when `x=<-1`

We stop going at the point `(-1,2)`

Similarly, since `f(x)=-2` when `x>=3`, all `y` values will be `-2` when `x>=3`

We stop going at the point `(3,-2)`

To find this function that is in the form `ax+b` and basically connect the two stop points, we simply find the equation of this connection using our formula `y-y_1=m(x-x_1)`

Our two points are: `(-1,2)` and `(3,-2)`

The slope is: `m=(-2-2)/(3-(-1))`

=>`m=(-4)/(4)`

=>`m=-1`

We now use our formula (We use `(-1,2)` as our `(x_1,y_1)`):

`y-2=-1(x-(-1))`

=>`y-2=-1(x+1)`

=>`y-2=-x-1`

=>`y=-x+1`

Comparing this to `ax+b`, we see that `a=-1` and `b=1`