Answer:
<h3>y + 2 = 3/7(x-7)</h3>
Step-by-step explanation:
The point-slope form of the equation will be expressed as;
y - y0 = m(x-x0) where;
m is the slope
(x0, y0) is the point on the line
Given
Slope m = 3/7
Point (x0, y0) = (7, -2)
Substitute into the equation;
y - y0 = m(x-x0)
y - (-2) = 3/7 (x - 7)
<em>y + 2 = 3/7(x-7)</em>
<em>Hence the equation in point-slope form is y + 2 = 3/7(x-7)</em>
Since g(6)=6, and both functions are continuous, we have:
![\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%20%3D%2045%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2B6f%28x%29%5D%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B9f%28x%29%5D%20%3D%2045%5C%5C%5C%5C9%5Ccdot%20lim_%7Bx%20%5Cto%206%7D%20f%28x%29%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20f%28x%29%3D5)
if a function is continuous at a point c, then
,
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
, f(6) = 5
Answer: 5
Remark
The quick answer is C does not represent a function. It has two y values for x = 2. These two points are (2,1) and (2,3). That eliminates C. No x can have 2 y values and be called a function. A function can have many x vales for a single y and still be a function.
A has all different x values, so it could be classed as a function. There are no values where x has more than 1 y value.
B also has all different x values. It too is a function.
Answer
A and B are both functions. C is not.
D <<<<< Answer
When adding/subtracting fractions you need a common denominator, but you already have one, which is x-3. So in general:
a/c-b/c=(a-b)/c so you just have:
(2x-6)/(x-3) now if you factor 2 from the numerator
2(x-3)/(x-3) the (x-3)s cancel out leaving
2
However! Note that division by zero is undefined, so x cannot equal 3. (because both original fractions had denominators of x-3)
What this all means is that that expression will equal 2 for all real values of x other than 3.
