6 Questions
What is the domain of a function that has a horizontal line?
All real numbers
For a function f(x) = |x|, what is the range of the function?
Non-negative real numbers
What is the domain of the function f(x) = √(x-3)?
x ≥ 3
What is the domain of the function f(x) = √(x-2)?
x ≥ 2
For the function g(x) = 1/x, what is the range?
y ≠ 0
What is the domain of the function h(x) = log(x+3)?
x > -3
Study Notes
Domain and Range of Functions
- The domain of a function that has a horizontal line is all real numbers (since it is defined for all values of x).
Absolute Value Function
- The range of the function f(x) = |x| is [0, ∞) since the absolute value function always gives a non-negative value.
Square Root Functions
- The domain of the function f(x) = √(x-3) is [3, ∞) since the expression inside the square root cannot be negative.
- The domain of the function f(x) = √(x-2) is [2, ∞) since the expression inside the square root cannot be negative.
Reciprocal Function
- The range of the function g(x) = 1/x is all real numbers except 0, since the function is never equal to 0.
Logarithmic Function
- The domain of the function h(x) = log(x+3) is (-3, ∞) since the argument of the logarithm function must be positive.
Test your knowledge of domain and range in mathematics with this quiz. Explore the domain of functions with horizontal lines, such as f(x) = c. Identify the range of the absolute value function f(x) = |x|. Determine the domain of functions with square roots, like f(x) = √(x-3).
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