Question

Please help with 7, 8, and 9, please put in step by step as this is a study guide for a test!

Answer 1

7. f(x) = -6/7x +12/7

8a. (-∞, -3)∪(-3, ∞); b. f(6) = 2/3

9a. f(-3) = -33; b. f(5a) = -50a² +25a

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.

`f(6)=(6)/(6+3)=(6)/(9)\\\\\boxed{f(6)=(2)/(3)}`

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9.

a. Put -3 where x is and do the arithmetic.

`f(-3)=-2(-3)^2+5(-3)=-2\cdot9-15\\\\\boxed{f(-3)=-33}`

b. Put 5a where x is and simplify.

`f(5a)=-2(5a)^2+5(5a)=-2(25a^2)+25a\\\\\boxed{f(5a)=-50a^2+25a}`