Answer:
(f · g)(x) = -6x² - 7x + 3
Step-by-step explanation:
To find the products, you have to first find the equations of the lines.
Red Line
First, find the slope. Use the following equation to find it.
[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]
Use the points marked on the line for the values.
[tex]m=\frac{-1-5}{-2-1}\\ m=\frac{-6}{-3} \\m=2[/tex]
Now, you need the y-intercept. The y-intercept is the point on the graph where the line crosses the y-axis. The line crosses the line at (0, 3). The y-intercept is 3.
Using y = mx + b form, the equation is g(x) = 2x + 3.
Blue Line
Find the slope the same way as above.
[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m = \frac{-5-1}{2-0}\\ m = \frac{-6}{2}\\ m=-3[/tex]
The line crosses the y-axis at (0, 1). The y-intercept is 1.
Using y = mx + b form, the equation is f(x) = -3x + 1.
Now multiply the two equations. Use the FOIL method (Front, Outer, Inner, Last).
(f · g)(x) = (2x + 3)(-3x + 1)
(f · g)(x) = -6x² + 2x - 9x + 3
(f · g)(x) = -6x² - 7x + 3
