how do i find the domain and range of equations?
example: f(x)=ab.solute value of x-3.
f(x)=square root 36-x^2
g(x)=-2x+2.
do i find the range by pluggin in y for the x and then solving. for example:
x=-2y+2, and then i get y=x-2/-2. and then is that how i find the range???????can i please have a detailed explanation:) thanks for your timeee
see your post from 4:00 pm
To find the domain and range of equations, we first need to understand what these terms mean.
The domain of an equation is the set of all possible input values or x-values for which the equation is defined. In other words, it specifies the values that x can take on in the equation.
The range of an equation is the set of all possible output values or y-values that the equation can produce. It represents the values the equation can attain.
Let's go through each equation and find their domain and range.
1. f(x) = a|b|(x-3):
In this equation, the domain is typically assumed to be all real numbers unless stated otherwise. Therefore, the domain is (-∞, ∞).
To find the range, we can analyze the structure of the equation. This equation has an absolute value function, which means the output is always non-negative. So, the range of this equation is [0, ∞).
2. f(x) = √(36 - x^2):
For this equation, we need to consider the domain carefully. The square root function is defined only for non-negative values. So we need to find the values of x that make 36 - x^2 non-negative.
To do this, solve the inequality 36 - x^2 ≥ 0. This inequality represents the condition for the square root to be defined. Solving it, we get -6 ≤ x ≤ 6. Therefore, the domain is the closed interval [-6, 6].
The range is determined by analyzing the graph of the equation, which is a semi-circle centered at the origin. The range is [0, 6].
3. g(x) = -2x + 2:
In this linear equation, the domain is again all real numbers because any x-value can be plugged into the equation.
To find the range, you can either analyze the graph (which is a straight line with a slope of -2), or you can express y in terms of x and observe that there are no restrictions on the values that y can take. Hence, the range is also all real numbers, or (-∞, ∞).
In summary:
- The domain of f(x) = a|b|(x-3) is (-∞, ∞), and the range is [0, ∞).
- The domain of f(x) = √(36 - x^2) is [-6, 6], and the range is [0, 6].
- The domain of g(x) = -2x + 2 is (-∞, ∞), and the range is (-∞, ∞).