Chapter 2.1 Practice

Questions

Question 1

  1. Determine the vector that moves the point \(p_1\) to the point \(p_2.\)
    1. \(p_1=(-1,2)\), \(p_2=(1,3)\)
    2. \(p_1=(3,4)\), \(p_2=(5,-1)\)
    3. \(p_1=(-1,-2)\), \(p_2=(-4,-6)\)
    4. \(p_1=(2,6)\), \(p_2=(5,9)\)

Question 2

  1. Evaluate these sums and explain their meaning:
    1. \(\langle 2,-3 \rangle +(1,3)\)
    2. \(\langle 1,4 \rangle +(0,2)\)
    3. \(\langle -3,-1\rangle +(-2,1)\)
    4. \(\langle -2,-5 \rangle +(-5,-4)\)

Question 3

  1. Take \(L\) to be the line with slope \(3\) and that intersects \((1,2).\)
    1. Identify a formula for the function \(L\).
    2. Identify a formula for the function \(\langle 2,5\rangle+L.\)

Question 4

  1. Take \(f\) to be the function given by the set of points \((x,y)\) in the plane that satisfy the equality \[ y=x^4.\]
    1. Sketch \(\langle -1,-3\rangle+f\).
    2. Identify a formula for the function \(\langle -1,-3\rangle+f.\)

Question 5

  1. Take \(f\) to be the function given by the set of points \((x,y)\) in the plane that satisfy the equality \[ y=\sqrt{x}.\]
    1. Sketch \(\langle -1,0\rangle+f\).
    2. Identify a formula for the function \(\langle -1,0\rangle+f.\)

Answers

Question 1

    1. \(V=\langle 2,1 \rangle\)
    2. \(V=\langle 2,-5 \rangle\)
    3. \(V=\langle -3,-4 \rangle\)
    4. \(V=\langle 3,3 \rangle\)

Question 2

    1. \((3,0)\); The point \((1,3)\) is moved by the vector \(\langle 2,-3\rangle\) to the point \((3,0).\) \(\langle 2,-3 \rangle +(1,3)\)
    2. \((1,6)\); The point \((0,2)\) is moved by the vector \(\langle 1,4 \rangle\) to the point \((1,6).\)
    3. \((-5,0)\); The point \((-2,1)\) is moved by the vector \(\langle -3,-1 \rangle\) to the point \((-5,0).\)
    4. \((-7,-9)\); The point \((-5,-4)\) is moved by the vector \(\langle -2,-5 \rangle\) to the point \((-7,-9).\)

Question 3

    1. \(L(x)=3(x-1)+2\) or \(L(x)=3x-1.\)
    2. \(f(x)=3(x-2)+4.\)

Question 4

    1. The sketch is shown below.
    2. \((x+1)^4-3\)

Question 5

    1. The sketch is shown below.
    2. \(\sqrt{x+1}\)

Return

© Copyright 2025 by the POC Writing Team: Bryan Carrillo, Yat Sun Poon, and David Weisbart. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the POC Writing Team.