Functions
Definition
Mathematical relationships between inputs (x-values) and outputs (y-values). They can be represented algebraically, graphically, or in tables.
Analogy
Think about functions as recipes. You input certain ingredients (x-values), follow specific instructions (mathematical operations), and obtain delicious outcomes (y-values).
Related terms
Domain: The set of all possible input values for which a function is defined.
Range: The set of all possible output values that result from evaluating a function.
Composite Function: A combination of two or more functions where the output of one function becomes the input of another.
"Functions" appears in:
Subjects (2)
Practice Questions (8)
What is the volume of the solid formed by revolving the region bounded by the functions f(x) = x^2 and h(x) = x + 1 around the x-axis from x = 0 to x = 1?
Consider a region defined by the functions g(x) = x^3 and h(x) = 2x^3, revolved around the x-axis from x = 0 to x = 2. What is the volume of the resulting solid?
What is the volume of the solid formed by revolving the region bounded by the functions g(x) = √x and h(x) = 2√x around the x-axis from x = 1 to x = 4?
Consider a region defined by the functions f(x) = 2x and h(x) = 3x, revolved around the x-axis from x = 0 to x = 2. What is the volume of the resulting solid?
What is the volume of the solid formed by revolving the region bounded by the functions g(x) = e^x and h(x) = 2e^x around the x-axis from x = 0 to x = 1?
Consider a region defined by the functions f(x) = x^2 and h(x) = 2x, revolved around the x-axis from x = 0 to x = 3. What is the volume of the resulting solid?
What is the volume of the solid formed by revolving the region bounded by the functions f(x) = x^2 and h(x) = x + 1 around the z-axis from x = 0 to x = 1?
What is the volume of the solid formed by revolving the region bounded by the functions f(x) = x^2 and h(x) = 3x around the z-axis from x = 1 to x = 2?
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