Okay, so I've never eally been clear on how to find domain and range of a function. Could someone explain how to get them then demonstrate on the problem \({4}^{2x}-5\)

AdamTaurus
Oct 13, 2017

#1**+1 **

4^{2x} - 5

This is an exponential.......the domain for an exponential is all real numbers [ note....2x is defined for all real numbers....so.....4^{2x} is, too....because the exponent is just a real number ]

The range is trickier.......if it was just 4^{2x} the range would be (0, infinity)

However.......the " - 5 " part shifts the graph down by 5 units.....so.....the range now becomes

(-5, infinity)

See the graph here : https://www.desmos.com/calculator/szmhu8kwjm

Notice that graph almost touches y = -5 [ but not quite !!!]

CPhill
Oct 13, 2017

#3**+2 **

y = - √ [ 2x -6]

First.....since we can't take the square root of something < 0....then 2x - 6 must be ≥ 0

So

2x - 6 ≥ 0

2x ≥ 6

x ≥ 3 and this is the domain → [3, infinity )

The range is a little tougher

The greatest value that y can be is when x = 3......which means that y = 0

Note that all x's greater than 3 produce a larger and larger square root....but...the " - " out front means that we gett larger and larger * negative* square roots......so......the range is actually

( - infinity, 0 ]

See the graph here : https://www.desmos.com/calculator/0mevks4btb

Note that as x* increases*, y

** **

CPhill
Oct 13, 2017