Graph included: hard limits are lim x--> 60- f(x) = 56; lim x--> 60+ f(x) = 68. what can you conclude about f(x)? how is this shown by the graph? the hard right and left limits are shown on the graph

I can conclude that f(x) has several jump discontinuities where the graph jumps from value to value, not having a gradual connecting curve that connects all of the points

it is shown by not having values from 32 to 44, jumping past the values between tem and other values
jumps from 32 to 44, skippinng the middle values

sorry for maybe confusing or lacking explanation

We can solve this problem using discriminant.

x^2-4x-12's discriminant is

(-4)^2-4*-12=16+48 which is clearly larger than 0

This means that it crosses over the axes 2 times.

In case you don't know what discriminant is, its in equation ax^2+bx+c

the discriminant is b^2-4ac.

If its positive it has 2 crosses with x axis, if negative then 0 crosses, if 0 then 1 cross.

Hope this helped at least a little bit :D