Antwoord  / Answer  1.1     
      
  
Vraag / Question 1.1  
  
  

  
Antwoord  / Answer  1.2     
      
  
Vraag / Question 1.2  
  
  

  
Antwoord  / Answer  1.3     
      
  
Vraag / Question 1.3  
  
  

  
Antwoord  / Answer  1.4     
      
  
Vraag / Question 1.4  
  
  

  
Antwoord  / Answer  1.5     
      
  
Vraag / Question 1.5  
  
  

  
Antwoord  / Answer  1.6     
      
  
Vraag / Question 1.6  
  
  

  
Antwoord / Answer 2.  
            f(x) = y = a.2^bx
                y = a.2^bx
                4 = a.2^b.0     . . .      y-afsnit / y-intercept (0;4)
                4 = a.1         . . .      2⁰ = 1
                a = 4
          ∴ f(x) = 4.2^bx
              16 = 4.2^b.(−2)     . . .      A(−2;16)
                4 = 2^b.(−2)
              2² = 2^(−2b)
                2 = −2b
                 −1 = b
          ∴ a = 4;  b = −1  en / and  f(x) = 4.2^−x
  
Vraag / Question 2.  
  
  

  
Antwoord / Answer 3.  
            f(x) = y = a.2^bx
           By / At A (0;1)  :  1 = a.2^b.0
                                         1 = a.1         . . .      2⁰ = 1
                                         a = 1
                                   ∴ f(x) = 2^bx
           By / At C (3;8)  :  8 = 2^b.3
                                       2³ =  2^b.3
                                       3b = 3
                                         b = 1
  
            g(x) = y = p.2^qx
           By / At B (0;−1)  : −1 = p.2^q.0
                                         −1 = p.1         . . .      2⁰ = 1
                                           p = −1
                                   ∴ g(x) = − 2^bx
           By / At D (−3;−8)  : −8 = − 2^q.(−3)
                                       − (2³) =  − 2^(−3q)
                                          −3q = 3
                                              q = −1
          ∴ a = 1;  b = 1  en / and  f(x) = 2^x  en / and   p = −1;  q = −1  en / and  g(x) = − 2^−x
  
Vraag / Question 3.  
  
  

  
Antwoord / Answer 4.  
          h(x) = 2^x − 2
  4.1  y = − 2
  
  4.2  By / At A : 2⁰ − 2  =  1 − 2
                                        = − 1
           A is die punt / the point (0;−1)
          By / At B : 2^x − 2  =  0
                                    2^x = 2
                                      x = 1
           B is die punt / the point (1;0)
  
  4.3  By / At P(p;30)  :  2^p − 2  =  30
                                                2^p = 32   = 2⁵
                                                  p = 5
           P is die punt / the point (5;30)
  
  4.3  h(x) ≤ 30  as / if  x ≤ 5
  
Vraag / Question 4.  
  
  

  
Antwoord / Answer 5.  
          f(x) = a.2^bx
  5.1  Y-afsnit / Y-intercept  (0;4)  : a.2^b(0)  =  4
                                                              a .1  =  4
                                                                  a  =  4
                                                                f(x) = 4.2^bx
          By / At P (−3 ; 32)  :  4.2^b(−3)  =  32
                                                    2^−3b = 8
                                                    2^−3b = 2³
                                                     −3b = 3
                                                         b = −1
           a = 4;  b = −1  en / and  f(x) = 4.2^−x
  
  5.2  Die grafiek word met 3 eenhede opwaarts geskuif  ⇒  y verander na (y − 3)
         The graph is moved 3 units upward  ⇒  y changes to (y − 3)
         ∴   f(x) = y = 4.2^−x  ⇒   y − 3 = 4.2^−x
                                                      y  = 4.2^−x + 3
                                                  g(x)  = 4.2^−x + 3
  
  5.3  Die grafiek word in die y-as gereflekteer    ⇒  (x ; y)  ⇒  (−x ; y)
         The graph is reflected in the y-axis               ⇒  (x ; y)  ⇒  (−x ; y)
                                                                    ∴  f(x) = y = 4.2^−x  ⇒   y  = 4.2^−(−x)
                                                                                                 ∴  h(x)  = 4.2^x
  
  5.4  Die grafiek word in die x-as gereflekteer    ⇒  (x ; y)  ⇒  (x ; −y)
         The graph is reflected in the y-axis               ⇒  (x ; y)  ⇒  (x ; −y)
                                                                    ∴  f(x) = y = 4.2^−x  ⇒   −y  = 4.2^−x
                                                                                                   ∴  k(x)  = − 4.2^x
  
Vraag / Question 5.  
  
  

  
Antwoord / Answer 6.  
          f(x) = p.2^−x + q
  6.1  q = 4   . . .   y =4 is die horisontale asimptoot / the horizontal asymptote.
  
  6.2  By / At D (−4 ; −12)  :  p.2⁻⁽⁻⁴⁾  + 4  =  −12
                                                     p .16 + 4  =  −12
                                                              16p  =  −16
                                                                   p  =  −1
                                                                 f(x) = 4 − 2^−x
  
  6.3  By / At  E (2 ; e)  :  e  =  4 − 2^−x
                                              =  4 − 2⁻²   =  4 − 0,25
                                              =  3,75
  
  6.4  f(x)  <  3,75  as / if  x  <  2
  
  6.5  f(x)  >  0  as / if  x  > x-afsnit.  /  x-intercept.
         f(x) = 0 as / if  4 − 2^−x  =  0
                                       2^−x  =  4  =  2²
                                         −x  =  2
                                           x  =  −2
         f(x)  >  0  as / if  x  > −2
  
Vraag / Question 6.  
  
  

  
Antwoord / Answer 7.  
          g(x) = 2^x + p  + q
  7.1  y-afsnit / y-intercept  :  2^0 + p  + q  = −1
                                                      2^p  + q  =  −1
                                                               q  =  −1  −  2^p
          By / At A (2 ; 11)       :  2^2 + p  + q  =  11
                                    2² . 2^p    −1  −  2^p  =  11      . . .  vervang q  /  substitute q
                                           2^p(4 − 1)  − 1  =  11      . . .  faktoriseer  /  factorise
                                                         3 . 2^p  =  12
                                                              2^p  =  4  =  2²
                                                                p  =  2
                                                                q  =  −1  −  2²
                                                                    =  −5
          ∴   g(x) = 2^x + 2  − 5
  
  7.2  Horisontale asimptoot / Horizontal asymptote  : y = −5
  
  7.3  Die grafiek word met 4 eenhede afwaarts geskuif  ⇒  y verander na (y + 4)
         The graph is moved 4 units downwards  ⇒  y changes to (y + 4)
         ∴   f(x) = y = 2^x + 2  − 5  ⇒   y + 4  =  2^x + 2  − 5
                                                              y  =  2^x + 2  − 5  − 4
                                                              y  =  2^x + 2  − 9
                                                          h(x)  =  2^x + 2  − 9
  
  7.4  Die grafiek word met 3 eenhede na regs geskuif  ⇒  x verander na (x − 3)
         The graph is moved 3 units to the right  ⇒  x changes to (x − 3)
         ∴   f(x) = y = 2^x + 2  − 5  ⇒   y  =  2^{(x − 3) + 2}  − 5
                                                        y  =  2^x − 1  − 5
                                                    k(x)  =  2^x − 1  − 5
  
  7.5  Die grafiek word in die y-as gereflekteer    ⇒  (x ; y)  ⇒  (−x ; y)
         The graph is reflected in the y-axis               ⇒  (x ; y)  ⇒  (−x ; y)
                                                           ∴  f(x) = y =  2^x + 2  − 5  ⇒   y  =  2^−x + 2  − 5
                                                                                               ∴  m(x)  =  2^−x + 2  − 5
  
Vraag / Question 7.  
  
  

  
Antwoord / Answer 8.  
          f(x) = y = 2^x
  8.1  Die grafiek word 3 eenhede afwaarts geskuif.  ⇒  y verander na y + 3
         The graph is moved 3 units downwards.  ⇒  y changes to y + 3
         ∴   f(x) = y = 2^x  ⇒ y + 3  = 2^x
         ∴   y  =  2^x  −  3
         ∴   g(x)  =  2^x  −  3
  
  8.2  Die grafiek word 2 eenhede na links geskuif.  ⇒  x verander na (x + 2)
         The graph is moved 2 units to the left.  ⇒  x changes to (x + 2)
          f(x) = y = 2^x  ⇒   y  =  2^x + 2
         ∴   h(x)  =  2^x + 2
  
  8.3  Die grafiek word in die y-as gereflekteer    ⇒  (x ; y)  ⇒  (−x ; y)
         The graph is reflected in the y-axis           ⇒  (x ; y)  ⇒  (−x ; y)
         ∴   f(x) = y =  2^x  ⇒   y  =  2^−x
         ∴  k(x) =  2^−x
  
Vraag / Question 8.  
  
  

  
Antwoord / Answer 9.  
          f(x) = y = 3^−x
  9.1  Die grafiek word 2 eenhede opwaarts geskuif.  ⇒  y verander na y − 2
         The graph is moved 2 units upward.  ⇒  y changes to y − 2
         ∴   f(x) = y = 3^−x  ⇒ y − 2  = 3^−x
         ∴   y  =  3^−x  +  2
         ∴   g(x)  =  3^−x  +  2
  
  9.2  Die grafiek word 4 eenhede na regs geskuif.  ⇒  x verander na (x − 4)
         The graph is moved 4 units to the right.  ⇒  x changes to (x − 4)
          f(x) = y = 3^−x  ⇒   y  =  3^−x − 4
         ∴   h(x)  =  3^−(x + 4)
  
  9.3  Die grafiek word in die x-as gereflekteer    ⇒  (x ; y)  ⇒  (x ; −y)
         The graph is reflected in the x-axis           ⇒  (x ; y)  ⇒  (x ; −y)
         ∴   f(x) = y =  3^−x  ⇒   −y  =  3^−x
         ∴  k(x) =  − 3^−x
  
Vraag / Question 9.  
  
  

  
Antwoord / Answer 10.  
            f(x) = y = 5^x + 3
  10.1  Die grafiek word 4 eenhede afwaarts geskuif.  ⇒  y verander na y + 4
           The graph is moved 4 units downwards.  ⇒  y changes to y + 4
           ∴   f(x) = y = 5^x + 3  ⇒ y + 4  = 5^x + 3
                                                 ∴   y  =  5^x + 3  −  4
           ∴   g(x)  =  5^x + 3  −  4
  
  10.2  Die grafiek word 4 eenhede na links geskuif.  ⇒  x verander na (x + 4)
           The graph is moved 4 units to the left.  ⇒  x changes to (x + 4)
            f(x) = y = 5^x + 3  ⇒   y  =  5^{(x + 4) + 3}
                                              y  =  5^x + 7
           ∴   h(x)  =  5^x + 7
  
  10.3  Die grafiek word in die y-as gereflekteer    ⇒  (x ; y)  ⇒  (−x ; y)
         The graph is reflected in the y-axis           ⇒  (x ; y)  ⇒  (−x ; y)
         ∴   f(x) = y =  5^x + 3   ⇒   y  =  5^(−x) + 3
         ∴  k(x) =  5^3 − x
  
Vraag / Question 10.  
  
  

  
Antwoord / Answer 11.  
            f(x) = − 3^−x + 2
  11.1  Die grafiek word 2 eenhede opwaarts geskuif.  ⇒  y verander na y − 2
           The graph is moved 2 units upward.  ⇒  y changes to y − 2
           ∴   f(x) = y = f(x) = − 3^−x + 2  ⇒ y − 2  = − 3^−x + 2
                                                                ∴   y  =  − 3^−x + 2  +  2
           ∴   g(x)  =  − 3^−x + 2  +  2
  
  11.2  Die grafiek word 3 eenhede na regs geskuif.  ⇒  x verander na (x − 3)
           The graph is moved 3 units to the right.  ⇒  x changes to (x − 3)
            f(x) = y = f(x) = − 3^−x + 2  ⇒   y  =  − 3^{−(x − 3) + 2}
                                                            y  =  − 3^−x + 5
           ∴   h(x)  =  − 3^−x + 5
  
  11.3  Die grafiek word in die x-as gereflekteer    ⇒  (x ; y)  ⇒  (x ; −y)
           The graph is reflected in the x-axis           ⇒  (x ; y)  ⇒  (x ; −y)
         ∴   f(x) = y = − 3^−x + 2  ⇒   − y  =  − 3^−x + 2
         ∴  k(x) =  3^− x + 2
  
Vraag / Question 11.