The intercepts are the points where the graph crosses the x or y-axes.
The y-intercept is -12, and the x-intercepts are 1, 2 and 6
The function is given as:
[tex]f(x) =x^3 - 9x^2 + 20x - 12[/tex]
Divide both sides by x - 6
[tex]\frac{f(x)}{x - 6} =\frac{x^3 - 9x^2 + 20x - 12}{x - 6}[/tex]
Factor the numerator
[tex]\frac{f(x)}{x - 6} =\frac{(x - 1)(x -2)(x - 6)}{x - 6}[/tex]
Cancel out x - 6
[tex]\frac{f(x)}{x - 6} =(x - 1)(x -2)[/tex]
Multiply both sides by x - 6
[tex]f(x) =(x - 1)(x -2)(x - 6)[/tex]
To calculate the y-intercept, we simply set x to 0
So, we have:
[tex]f(0) =(0 - 1)(0 -2)(0 - 6)[/tex]
[tex]f(0) =-12[/tex]
To calculate the x-intercept, we set f(x) to 0.
so, we have:
[tex](x - 1)(x -2)(x - 6) =0[/tex]
Solve for x
[tex]x = 1\ or x = 2\ or\ x = 6[/tex]
Hence, the y-intercept is -12, and the x-intercepts are 1, 2 and 6
Read more about intercepts at:
https://brainly.com/question/5313581
