Question

Choose which function is represented by the graph A. f(x) = (x - 1)(x + 2)(x+5)(x+10)

B. f(x) = (x - 5)(x-2)(x + 1)
C. f(x) = (x - 10)(x - 5)(x - 2)(x+1)
D. f(x) = (x - 1)(x + 2)(x+5)

Answer 1

Option B

Explanation:

From the graph attached,

x-intercepts of the graph are x = -1, 2 and 5

y-intercept of the graph is y = 10

Since, x intercepts of a graph define the zeros of the function (y = 0)

Therefore, (x + 1), (x - 2) and (x - 5) are the zero factors of the given graphs.

And the equation of the function will be,

f(x) = a(x + 1)(x - 2)(x - 5)

Since, -intercept of the function is y = 10

Therefore, for x = 0,

y = a(0 + 1)(0 - 2)(0 - 5) = 10

a(10) = 10

a = 1

So the function representing the graph is,

f(x) = (x - 1)(x + 2)(x - 5)

Option B will be the answer.