Question

What are the points of intersection between the graphs of the functions f(x) = (x-3)(x+1) and g(x) = x+1 ?

Answer 1

To find the points of intersection between the functions f(x) = (x-3)(x+1) and g(x) = x+1, we set them equal and solve for x. The points of intersection are at (4,5) and (-1,0).

Step-by-step explanation:

To find the points of intersection between the graphs of the functions f(x) = (x-3)(x+1) and g(x) = x+1, we need to set the functions equal to each other and solve for x.

First, we shall simplify f(x):
f(x) = (x-3)(x+1) = x2 - 3x + x - 3 = x2 - 2x - 3.

Next, we set f(x) equal to g(x) and solve for x:

1. x2 - 2x - 3 = x + 1
2. x2 - 3x - 4 = 0
3. (x - 4)(x + 1) = 0
4. x = 4 or x = -1.

Now, we substitute these x-values back into either f(x) or g(x) to find the corresponding y-values.

• For x = 4: g(4) = 4 + 1 = 5, so one point of intersection is (4,5).
• For x = -1: g(-1) = -1 + 1 = 0, so the other point of intersection is (-1,0), which is actually the point where both graphs touch each other as g(x) is a factor of f(x).

Therefore, the points of intersection are (4,5) and (-1,0).