Question 7 Create an R function \texttt{pwfun()}, which computes values of the piece-wise (mathematical) function \texttt{pwfun} defined in the following way: Its graph is as follows. $$\text{pwfun}(x) = \begin{cases} -2x - 2, & x < -1\\ 0, & -1 \le x \le 1\\ x^2 - 1, & 1 < x \end{cases}$$ Your R function \texttt{pwfun()} should also accept \texttt{x} as a vector of arbitrary length and return vector of the same length with entries defined as values of the mathematical function \texttt{pwfun}, evaluated at the corresponding entries of vector \texttt{x}. Here are some input vectors and what you should get as a corresponding output. \texttt{pwfun}(-1) 0 \texttt{pwfun}(c(-2, 0.5, 3)) 2 0 8 x = c(-3, -2, -1, 0, 1, 2, 3.2) \texttt{pwfun}(x) 4 2 0 0 0 3 9.24
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Match the objects on the left with one or more of the descriptions on the right. Explain your choice. 1. |<1,3,4> × <2,-1,3>| 2. |i j k| |1 3 4| |2 -1 3| 3. (a × b) · c, where a = <1,3,4>, b = <2,-1,3> and c = 4. 4. (a · b) / (|a||b|), where a = <1,3,4>, and b = <2,-1,3> 5. (a · b) × c, where a = <1,3,4>, b = <2,-1,3> and c = <3,2,7> 6. r(t) = <2,-1,3> + t <1,3,4> 7. The set of points satisfying (x - 2) / 1 = (y + 1) / 3 = (z - 3) / 4 8. x + 3y + 4z = <3,2,7> 9. <1,3> · <x - 3, y - 2> = 0 10. The intersection of the graphs of 2x - 2y + z = 9 and 11x + 7y - 8z = -9 a. This thing doesn't make sense. b. A scalar c. A vector d. A scalar function e. A vector function f. A vector perpendicular to both <1,3,4> and <2,-1,3> g. The area of a parallelogram whose edges are the vectors a = <1,3,4>, b = <2,-1,3> h. The volume of a parallelepiped, with edges a, b, c i. The cosine of the angle between a and b j. A line in the direction <1,3,4> k. A line in 3-space l. A function mapping R to R^3 m. The line 3y + x = 9, lying in the xy-plane
Sri K.
Another strategy for graphing a piecewise function is to use a table of values. The table below has a column for the input values x and for each piece of the function. The shaded cells indicate where the pieces do not define the function for those input values, so you do not need to find those values. You will need to decide which piece is used to define the function when x=3.
Bailey C.
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