Question

Supose you have a linear transformationf: ℝ → ℝ, wheref(3) = 9 andf(5) = 15.

1. Use the adition property to computef(8) andf(13).
2. Findf(12) andf(10). Show your work.
3. Findf(−3) andf(−5). Show your work.
4. Findf(0). Show your work.
Find a formula forf(x).
6. Draw the graph of the function y =f(x).

Answer 1

Lets take

f(x) = a x +b

x= 3 ,f(3)=9

9 = 3 a + b ------------1

x=5 ,f(5) = 15

15 = 5 a + b ---------2

From equation 1 and 2

6 = -2 a

a = - 3

9 = 3 (-3)+ b

b= 18

f(x) = -3 x + 18

f(8) = -3 x 8 + 18=-24 + 18 = -6

f(13) = -3 x 13+ 18 = - 39 + 18 =-11

f(12) = -3 x 12+ 18 = - 36 + 18 = -18

f(10) = -3 x 10 + 18 = -12

f(-3) = -3 x (-3)+ 18 =27

f(-5) = -3 x (-5)+ 18 = 33

f(0) = -3 x 0+ 18 = 18

Answer 2

Lets take

f(x) = a x +b

x= 3 ,f(3)=9

9 = 3 a + b ------------1

x=5 ,f(5) = 15

15 = 5 a + b ---------2

From equation 1 and 2

6 = -2 a

a = - 3

9 = 3 (-3)+ b

b= 18

f(x) = -3 x + 18

f(8) = -3 x 8 + 18=-24 + 18 = -6

f(13) = -3 x 13+ 18 = - 39 + 18 =-11

f(12) = -3 x 12+ 18 = - 36 + 18 = -18

f(10) = -3 x 10 + 18 = -12

f(-3) = -3 x (-3)+ 18 =27

f(-5) = -3 x (-5)+ 18 = 33

f(0) = -3 x 0+ 18 = 18