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Functions

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AP Calculus AB/BC

Definition

Mathematical relationships between inputs (x-values) and outputs (y-values). They can be represented algebraically, graphically, or in tables.

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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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