# How do we find the values of k and m that makes function continue anywhere piecewise function of #(x^2) + 5# when x > 2, #m(x+3) + k# when #-1 < x <=2# and #2(x^3) + x + 7# when #x <=-1#?

##### 2 Answers

#### Explanation:

Here is an example of a continuous function.

Here is an example of a discontinuous function.

So, continuous functions are where everything is connected; there are no gaps or holes.

The y-value of

We need the graph of

The

We need the graph of

Hence, we can write a systems of equations with respect to

So, the function in the interval

#### Explanation:

We want to find

Just think about what we know so far, and how it would look:

When

When

So for the mid interval we need a straight line whose equation is

This line would have the following gradient:

So our required line passes through

So the mid-section has equation

ie