Question

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:​

Answer 1

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

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

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).