Which function does the graph represent? f(x) = (x + 3)(x + 7) f(x) = (x – 3)(x – 7) f(x) = 3(x – 3)(x – 7) f(x) = 11(x + 3)(x + 7)

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)

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)

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answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

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