Functions and weird equation

Question

 

I am not quite sure what this is. I am horrible at Math, and my teacher doesn't give me answer key to his test.

Answer 1

18) The function f(x) = 3x + 5

Difference quotient is [ f(x + h) - f(x) ]/h

f(x + h) = 3( x + h) + 5 = 3x + 3h + 5

[ f(x + h) - f(x) ]/h = [ (3x + 3h + 5) - (3x + 5) ]/ h

= [ 3x + 3h + 5 - 3x - 5 ]/h

= 3h /h

= 3

 [ f(x + h) - f(x) ]/h = 3.

Answer 2

19) The rational function

Change f (x ) to y .

Simplify the rational function.

Factorize the numarator.

x ² - 11x  +18 

= x ² - 9x  - 2x  +18 

= x (x  - 9) - 2 (x  - 9)

= (x  - 9) (x  - 2)

Now the function is y  = x  - 2.

The equation of the line y  = x  - 2.

To find the hole of the function equate x  - 9 = 0

x  = 9

Substitute x  = 9 in linear function y  = x  - 2

y  = 9 - 2

y  = 7

Coordinates of hole (x , y ) = (9, 7).