Mathematical relationships between inputs (x-values) and outputs (y-values). They can be represented algebraically, graphically, or in tables.
Think about functions as recipes. You input certain ingredients (x-values), follow specific instructions (mathematical operations), and obtain delicious outcomes (y-values).
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.
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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