Final answer:
To find the points of intersection between the graphs of f(x) and g(x), set f(x) = g(x) and solve for x. The solutions are x = -5 and x = 4. Substitute these values back into either function to find the corresponding y-values, yielding the intersection points (-5, 0) and (4, 9).
Step-by-step explanation:
To find the points of intersection between the graphs of the functions f(x) = (x + 5)(x – 4) and g(x) = x + 5, we need to set them equal to each other and solve for x. This is because at the points of intersection, both functions will have the same y-value (the dependence of y on x is the same for both functions).
Setting f(x) equal to g(x):
(x + 5)(x - 4) = x + 5
Expanding f(x):
x^2 + 5x - 4x - 20 = x + 5
Combining like terms:
x^2 + x - 20 = x + 5
Subtracting x + 5 from both sides:
x^2 - 20 = 0
Factoring the quadratic equation:
(x + 5)(x - 4) = 0
Setting each factor equal to zero gives us two solutions:
x + 5 = 0 or x - 4 = 0
Thus, x = -5 or x = 4.
To find the corresponding y-values, we substitute these x-values back into either original function (using g(x) for simplicity):
For x = -5: g(-5) = -5 + 5 = 0
For x = 4: g(4) = 4 + 5 = 9
Therefore, the points of intersection are (-5, 0) and (4, 9).