Which of the following best represents the relationship between functions f and g? g(x) = -f(x) - 1
g(x) = f(x - 1)
g(x) = -f(x) + 1
g(x) = -f(x)

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  (c)  g(x) = -f(x) +1

Step-by-step explanation:

We really only need to consider one point on f(x) and/or g(x). We can look at the y-intercepts.

  f(0) = 4  and  g(0) = -3

Looking at the answer choices, we see ...

  A. -f(0) -1 = -4 -1 = -5 ≠ g(0)

  B. f(0 -1) = f(-1) = 1 ≠ g(0)

  C. -f(0) +1 = -4 +1 = -3 = g(0) . . . . . matches requirements

  D. -f(0) = -4 ≠ g(0)

The relation between f(x) and g(x) is g(x) = -f(x) +1.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)