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

The answer is A because the points that are represented given where they intercept on the x and y axis. These points are -1, 2, 10, and 5

Answer 2

The correct function represented by the given graph is:

A. f(x) = (x - 1)(x + 2)(x + 5)(x + 10).

To determine which function is represented by the given graph, we need to analyze the characteristics of the graph and compare them to the factors in each of the provided functions.

The graph of a polynomial function intersects the x-axis at points corresponding to the roots of the polynomial. Each root is associated with a factor in the polynomial.

Looking at the given options:

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)

We observe that the graph intersects the x-axis at x = 1, x = -2, x = -5, and x = -10. These values correspond to the roots of option A. Therefore, the correct answer is:

A. f(x) = (x - 1)(x + 2)(x+5)(x+10)

This polynomial function has roots at x = 1, x = -2, x = -5, and x = -10, matching the characteristics of the given graph.