Answer:
(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 [tex]\:x < 2\quad \mathrm{or}\quad \:x > 2\:[/tex]
In interval notation [tex]\:\left(-\infty \:,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]
(e) x intercept is at x = -7
(f) y-intercept is at [tex]-\frac{7}{2} = -3.5[/tex]
Step-by-step explanation:
(b) Plug in x = 1 into the equation [tex]\:\:\frac{x+7}{x-2} = \frac{1+7}{1-2} = \frac{8}{-1} = -8[/tex]
(c) If f(x) = 2 then we get [tex]2 = \:\:\frac{x+7}{x-2}[/tex]
==> 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) [tex]y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0[/tex]
Substitute for x = 0 to get y = (0+7)/(0-2) = -7/2
