Respuesta :
Answer with Step-by-step explanation:
We are given that a function
[tex]f(x)=x^3-x^2-17x-15[/tex]
We have to find the graph of the given function.
y-intercept:It is that value of y where the graph cut the y- axis.
Let
[tex]y=f(x)=x^3-x^2-17x-15[/tex]
Substitute x=0
Then, we get
[tex]f(0)=-15[/tex]
y-intercept of the graph=-15
x- intercept: It is that value of x where the graph cut the x- axis.
Substitute y=0
[tex]x^3-x^2-17x-15=0[/tex]
Substitute x=-1
[tex]-1-1+17-15=0[/tex]
Therefore,x=-1 is a solution of given equation.
[tex](x+1)(x^2-2x-15)=0[/tex]
[tex](x+1)(x^2-5x+3x-15)=0[/tex]
[tex](x+1)(x(x-5)+3(x-5))=0[/tex]
[tex](x+1)(x+3)(x-5)=0[/tex]
[tex]\implies x=-1,-3,5[/tex]
Hence, the x-intercept are
-3,-1 and 5
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