Question

Can someone help me with this

Answer 1

(a) Choice C is correct

(b) f(x) = -8 Point is (1, -8)

(c) x =11 Point is at (11,2)

(d) Domain of f is x is
`\:x < 2\quad \mathrm{or}\quad \:x > 2\:`
In interval notation
`\:\left(-\infty \:,\:2\right)\cup \left(2,\:\infty \:\right)`

(e) x intercept is at x = -7

(f) y-intercept is at
`-(7)/(2) = -3.5`

Explanation:

(b) Plug in x = 1 into the equation
`\:\:(x+7)/(x-2) = (1+7)/(1-2) = (8)/(-1) = -8`

(c) If f(x) = 2 then we get
`2 = \:\:(x+7)/(x-2)`

==> 2(x-2) = x + 7

==> 2x - 4 = x + 7

==> 2x - x = 7 +4 =11

==> x = 11

(d) Domain of f is all values of x -∞ < x < ∞ except at x = 2 since at x = 2 the denominator is 0 and division by zero is undefined; So we can say the domain is x < 2 or x >2

(e) To get the x-intercept set y = 0 and solve for x
We get (x+7)/(x-2) = 0

x+7 = (x-2)(0) = 0

x = -7 and the x intercept is at point (-7, 0)

(f)
`y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0`

Substitute for x = 0 to get y = (0+7)/(0-2) = -7/2

Answer 2

b) -8

c) 11

d) x is a member of all real numbers