This question is incomplete because it lacks the picture of the graph. Find attached to the answer, the picture of the graph.
Question:
Which function does the graph represent?
a) f(x) = (x + 3)(x + 7)
b) f(x) = (x – 3)(x – 7)
c) f(x) = 3(x – 3)(x – 7)
d)f(x) = 11(x + 3)(x + 7)
Answer:
c) f(x) = 3(x – 3)(x – 7)
Step-by-step explanation:
The function of a graph or the the graph of a function is when
f(x) = y
From the attached graph, after reading it,
They are three specific points on the x - axis, where x = 3 and x = 7, x = 8
So, where x = 3 on the x axis, y =
f(3) = 0
where x = 7 on the x axis, y =
f(7) = 0
So, where x = 8 on the x axis, y =
f(8) = 15
Looking at the options in the question,
a) f(x) = (x + 3)(x + 7)
f(x) = y
where x= 3
f(3) = (3+3)(3+7)
= 60
where x= 7
f(7) = (7+3)(7+7)
= 140
where x= 8
f(8) = (8+3)(8+7)
= 165
This option is wrong
b) f(x) = (x – 3)(x – 7)
f(x) = y
where x= 3
f(3) = (3-3)(3-7)
= 0
where x= 7
f(7) = (7-3)(7-7)
= 0
where x= 8
f(8) = (8-3)(8-7)
= 5
This option is wrong.
c) f(x) = 3(x – 3)(x – 7)
f(x) = y
where x= 3
f(3) = 3(3-3)(3-7)
= 0
where x= 7
f(7) =3(7-3)(7-7)
= 0
where x= 8
f(8) = 3(8-3)(8-7)
= 3(5)(1)
= 15
This option is correct
d)f(x) = 11(x + 3)(x + 7)
f(x) = y
where x= 3
f(3) = 11(3+3)(3+7)
= 660
where x= 7
f(7) = 11(7+3)(7+7)
= 1540
where x= 8
f(8) = 11(8+3)(8+7)
= 1815
Therefore, function the graph represents is Option c) f(x) = 3(x – 3)(x – 7)
