1) What is a vector-valued function? a) A function that assigns a scalar to another scalar. b) A function that assigns a real number to a vector. c) A function that assigns a vector to another vector. 2) Given r(t)=<3t,2t2,t3>, in which space is its range located? a) R2 b) R3 c) R 3) Observe the graph. Which vector function could represent it? a) <t,t2> b) <cos t, sin t> c) < et, t> 4) Evaluate <sin t, cos t > when t=π/2. a) ⟨1, 0⟩ b) ⟨0, 1⟩ c) ⟨0, −1⟩ 5) The domain of a vector-valued function is defined as: a) The set of all input values t that make each component defined. b) The range of the first component. c) The set of all possible vectors. 6) Geometrically, what does a vector-valued function in space represent? a) A surface. b) A point. c) A curve or path traced by the tip of the position vector. 7) If r(t) = <e^t, ln(t), t^2>, for what values of t is it defined? a) t>0 b) all real numbers c) t<0 8) The following image shows a circular trajectory in the xy-plane. Which of these functions describes it? a) ⟨t, t²⟩ b) ⟨e^t, t⟩ c) ⟨cos t, sin t⟩ 9) Compute the derivative of r(t)=<t², 3t, e^t> a) ⟨t, 3t², e^t⟩ b) ⟨2t,3,e^t⟩ c) ⟨2, 3, e^t⟩ 10) What is the physical interpretation of the derivative of a position vector function? a) It represents velocity. b) It represents acceleration. c) It represents the initial position. 11) If r(t)=< 2t, t^2 >, what does < 0, 2 > represent? a) The velocity vector at each point of the path. b) The initial position. c) The acceleration vector at each point 12) If the magnitude of r'(t) remains constant, what type of motion does the object have? a) Motion with constant acceleration. b) Motion with constant speed. c) Non-uniform circular motion. 13) Observe the spiral curve shown. Which vector function could describe it? a) r(t) = < t, t^2, t^3> b) r(t) = < cos t, sin t, t> c) r(t) = <e^t, ln t, t> 14) Before programming a vector-valued function in MATLAB, what should students clearly understand? a) Only the syntax of the software. b) The color and all the possible editions that I want for the plot. c) The domain of t, the components, the geometric interpretation, and how to derive them.

Vector Functions

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