this is a removable discontinuity
Here we have the piecewise function:
[tex]f(x) = \frac{-4x}{x - 3}[/tex] if x < 5
[tex]f(x) = -7x + 25[/tex] if x > 5.
We want to see which type of discontinuity we have at x = 5.
Remember that:
If we have two asymptotes, then is an infinite discontinuity
if just one point is missing, then it is a removable discontinuity
If the value drastically changes after the discontinuity, then its a jump discontinuity
Mixed case is when two of these happen.
Because we have a piecewise function, we need to evaluate both parts in x = 5.
If both parts give the same value, then we will have a removable discontinuity
if the values are different, then we have a jump discontinuity.
first part:
f(5) = -4×5/(5 - 3) = -20/2 = -10
second part:
f(5) = -7×5 + 25 = -35 + 25 = -10
So we got the same value, which means that this is a removable discontinuity
in the image below you can see the graph of the piecewise function, and see that as x tends to 5, both sides of the function tend to the same value.
if you want to read more about this,, you can see:
https://brainly.com/question/17317969
