# Find the values of m and b that make f continuous everywhere: m = ? b = ?

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#f(x) = {((7+6x-x^2)/(x+1)",", x < -1),(mx+b",", x ∈ [-1,4]),(2*2^(4-x)+16",", x>4):}#

Have never seen a piecewise function quite like this before and not sure how to even graph the mx+b line in all honesty.

#f(x) = {((7+6x-x^2)/(x+1)",", x < -1),(mx+b",", x ∈ [-1,4]),(2*2^(4-x)+16",", x>4):}#

Have never seen a piecewise function quite like this before and not sure how to even graph the mx+b line in all honesty.

##### 1 Answer

#### Explanation:

We can see that each individual function will be continuous on their domains.

To ensure that the function is continuous, we have to find the values of

First looking at

At

So, we need

We can't solve explicitly for

At

So, we have the two relations of

#{(-m+b=8),(4m+b=18):}#

Solving this gives:

#{(m=2),(b=10):}#