+895 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 \({4}^{2x}-5\)
+128460 42x - 5
This is an exponential.......the domain for an exponential is all real numbers [ note....2x is defined for all real numbers....so.....42x is, too....because the exponent is just a real number ]
The range is trickier.......if it was just 42x 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 !!!]
+128460 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 decreases
