Answer:
7. f(x) = -6/7x +12/7
8a. (-∞, -3)∪(-3, ∞); b. f(6) = 2/3
9a. f(-3) = -33; b. f(5a) = -50a² +25a
Step-by-step explanation:
7. You are given two points: (2, 0), (-5, 6). It is often useful to start with the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (6 -0)/(-5-2)(x -2) +0
y = -6/7(x -2) . . . simplify
y = -6/7x +12/7 . . . slope-intercept form
f(x) = -6/7x +12/7 . . . . the desired functional form
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8.
a. The domain is the set of x-values for which the function is defined. It will be undefined when the denominator is zero. So, the domain is all real numbers except x=-3. That can be written as ...
-∞ < x < -3 ∪ -3 < x < ∞
b. Put 6 where x is and do the arithmetic.
[tex]f(6)=\dfrac{6}{6+3}=\dfrac{6}{9}\\\\\boxed{f(6)=\dfrac{2}{3}}[/tex]
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9.
a. Put -3 where x is and do the arithmetic.
[tex]f(-3)=-2(-3)^2+5(-3)=-2\cdot9-15\\\\\boxed{f(-3)=-33}[/tex]
b. Put 5a where x is and simplify.
[tex]f(5a)=-2(5a)^2+5(5a)=-2(25a^2)+25a\\\\\boxed{f(5a)=-50a^2+25a}[/tex]
