Can anybody help me write the equation of the function from the graph? Thanks

enter image source here

1 Answer
Feb 12, 2018

f(x) = -1/2(x-3)(x+3) for x in [-3,+3]
f(x)=1/2(x-3) for x in (3,5]

Explanation:

From the picture we can see that f(x) is a piecewise function.

I will assume that the domain of f(x) is entirely shown in the picture.

:. Domain of f(x) is [-3,+5] with subdomains [-3,+3] and (+3,+5]

By sight f(x) appears to be a parabola in [-3,+3]
and a straight line in (+3,+5]

I will assume to above to be true.

We can see that f(x) has zeros at x=-3 and x=3

Hence, we can say that a(x-3)(x+3)=0 for some constant a

We can also observe that f(0) = 9/2

:. a(+3)(-3) =9/2 -> a =-1/2

Hence, f(x) = -1/2(x-3)(x+3) for x in [-3,+3]

Then, for x in (3,5] we have f(x) = mx +c (a straight line with slope m)

From the picture: m = 1/(5-3) = 1/2

Finally, we can see that f(x) = 1 at x=+5

:. 1=1/2xx5 +c -> c =-3/2)

f(x) = 1/2x-3/2 for x in (3,5]

Hence, f(x)=1/2(x-3) for x in (3,5]