Which of the following transformations will change the range of exponential functions? a Vertical Compression b Vertical Shift c Horizontal Shift d None of the above

Step-by-step explanation:

Remember that the range is the set value that defined the dependent variable  of a function, which is represents with Y.

So, all transformations about vertical shifts, it would represent a change to the range set of the exponential fuction.

For example, let's say that we have the function , which domain is all real numbers and which range is all real numbers greater than zero.

Now, let's say we transform that function to , which is the same function but shifted up 6 units.

Notice that the function has the same domain -all real numbers- but different range, because it's defined by all real numbers greater than 6.

Therefore, the transformation that can change the range of a function is B. Vertical Shift.

the correct answer is 5 6 and 7

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!