x < 3
x is greater than or equal to 3
They give you the table and also give you the numbers.
For x < 3
You will look at numbers that are smaller than 3 ( in the table, 1 and 2 is smaller than 3) You will put log 1 in 9 - x^2
9 - (1)^2
9 - 1 = 8
Do the same way for 2.
9 - (2)^2
9 - 4 = 5
x is greater than or equal to .
You will find the numbers which greater than or equal to 3. (in this table, 3, 4, 5 are the numbers that are greater than or equal to 3)
You will log 3 in x - 3
3 - 3 = 0
Do the same thing with 4 and 5
3 - 4 = -1
3 - 5 = -2
I hope this helps!
answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4
polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!
complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.
the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7
verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.
a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.
you 're wlecome! : )
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