Without graphing, determine the range of the function f(x) = 4|x+6|-5 over the interval [-10,5].

[-5,39]

Step-by-step explanation:

The vertex is at (-6,-5)

The interval is from -10 to 5 (inclusive of both endpoints...

Absolute function is open up because 4 is positive

I will plug in both endpoints now:

f(-10)=4|-10+6|-5                               f(5)=4|5+6|-5

f(-10)=4(4)-5                                      f(5)=4(11)-5

f(-10)=11                                             f(5)=39

So the highest reached by f(5) which is 39 so our range will go up to 39 (inclusive)

11 is not the lowest reached, -5 is because our vertex was included within the domain

So the range is [-5,39]

a is the correct