20. A linear function is shown.

f (x) = (-5/2) x - 3

A. Create a linear function g (x) such that f (x) = g (x) has exactly one solution.

B. What is the exact solution to f (x) = g (x) ?

Answer A:

Answer B:

g (x) = (1/2) x + 3

f (x) = g (x) at (-1/2, 13/4)

Step-by-step explanation:

g (x) and f (x) will have exactly one solution when they are not parallel (same slope) and when they are not equivalent functions (like doubling or halving all terms).

f (x) = (-5/2) x - 3

g (x) = (1/2) x + 3 < = choose an easy equation.

To find the solution, equate the two functions:

f (x) = g (x)

(-5/2) x - 3 = (1/2) x + 3

(-5/2) x - (1/2) x = 3 + 3 < = move variables to one side, constants to other

(-6/2) x = 6 < = simplify

x = 6 / (-6/2) <=isolate x

x = - 6/12

x = - 1/2

Substitute x = - 1/2 into any equation to find y

g (x) = (1/2) x + 3

g (1/2) = (1/2) (1/2) + 3

g (1/2) = (1/4) + 3

g (1/2) = (1/4) + (12/4) < = find common denominator to add

y = (13/4) < = the function symbol can be replaced by y

The coordinates are (-1/2, 13/4).