Domain and Range

Check if there are fractions in the equation.

After you've placed all the terms that contain "x" on one side of the equation...

(a+b)+c=a+(b+c) (2+5)+3=2+(5+3)

Associative Property of addition

a+b=b+a 2+5=5+2

Commutative Property of Addition

a(b+c)=ab+ac 2(5+3)=2*5+2*3

Distributive Property of Multiplication over addition

The function g(s)=√3-s ​ ​is not defined for real numbers greater than 3, which would result in imaginary values for g(s). Hence, the domain for g(s) is "all real numbers, s ≤ 3"

How can I find the domain of g(s)=√3-s ?

Domain: The function is defined for all real values of x (because there are no restrictions on the value of x). Hence, the domain of f(x) is "all real values of x". Range: Since x^2 is never negative, x2 + 2 is never less than 2 Hence, the range of f(x) is "all real numbers f(x)≥2"

How can I find the domain of the function f(x) = x^2 + 2 ?

1.- you have a fraction, so you need to check first if there is a chance of having zero in the denominator. 2.- solve for t+2 = 0 t= -2 hence, t cannot take the value of -2 , for it would be impossible to divide over zero. The domain is all the real numbers except -2

How can I find the domain of the function ​f(t) = 1/(t+2) ​​

When finding the domain, remember: The denominator (bottom) of a fraction cannot be zero The number under a square root sign must be positive in this section

If I'm given a function, what should I look for in order to find the domain?

eliminate them by finding the common denominator.

If there are fractions in the equation

Generally, negative values of time do not have any meaning. Also, we need to assume the projectile hits the ground and then stops - it does not go underground. So we need to calculate when it is going to hit the ground. This will be when h = 0. So we solve: 20t − 4.9t^2 = 0 Factoring gives: (20 − 4.9t)t = 0 This is true when t=0 seconds or t= 20/ 4.9 = 4.082 seconds ​ Hence, the domain of the function h is "all real values of t such that 0 ≤ t ≤ 4.082"

Let's apply it to real life! We fire a ball up in the air and find the height h, in metres, as a function of time t, in seconds, given by h = 20t − 4.9t ^2 Find the domain for the function h(t).

The complete set of possible values of the independent variable. The set of all possible x-values which will make the function "work", and will output real y values

What is the domain of a function?

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. The range is the resulting y-values we get after substituting all the possible x-values.

What is the range of a function?

Start by placing all the terms that contain an x on one side of the equation.

What should you do in order to start solving the value of a variable in an equation?