i just cannot seem to wrap my head in this.
im supposed to take a function like
y = 4x-6.2
and state its domain and range which from what my notes tell me is supposed to look like
D = {X|XER}
R = {Y|YER}
but i cant seem to find a way to start or solve it , anyone got an ideal? thanks for any help.
First, the implicit assumption is that, unless otherwise specified, we're talking about real numbers.
Are there any real values of x for which the function is not a real number? Those values are not in the domain; all other values are.
Are there any real values that y cannot have? Those values are not in the range; all other values are.
Example 1: \(\displaystyle y = \sqrt{x} - 1.\)
If x is negative, the square root of x is not defined in the real numbers. The domain is all non-negative numbers. Because the square root of x is not less than zero, y cannot be less than - 1. The range is all real numbers greater than or equal to -1.
Example 2: \(\displaystyle y = \left | \dfrac{1}{x^2 + 5x + 6} \right | + 2.\)
Here x cannot equal x = - 2 or - 3, which would make the denominator zero and render the function undefined in the real numbers. So the domain is all real numbers except -2 and -3. Obviously, y cannot equal 2, nor can it be less than 2. So the range is all real numbers greater than 2.
