Where does
sec x = 0
and
tan x = 0?sec x cannot ever be zero, but tan x = 0 when sin x = 0 Chuck norris can make sec x 0
All of these are values of x ....-2pi, -pi, 0, pi, 2pi, 3pi, ....
The graph shows a
piecewise function, meaning that different functions are shows at different intervals (ranges of x-values).
1) One of the graphs is part of a parabola, meaning the equation is quadratic (has
![x^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20)
). That equation must be
![x^{2} + 4](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B%204)
.
2) The other graph is a straight line, meaning it must be a linear equation. That equation must be x + 4.
Looking at the entire graph, you can see that the parabola starts from the left and ends with an open circle at x=2. An open circle means that the graph doesn't have a value at that point, x=2. The linear line starts with a filled point at x=2 and continues to the right. That means we're looking for the choice where:
1)
![x^{2} + 4 \ \textless \ 2](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%204%20%20%5C%20%5Ctextless%20%5C%20%202)
Since x=2 cannot be a point in the graph, and less than 2 means that the graph includes everything to the left of 2, but not including 2
2)
![x + 4 \geq 2](https://tex.z-dn.net/?f=x%20%2B%204%20%20%5Cgeq%20%202)
Since x=2 is a point in the graph, and greater than or equal to 2 means that the graph includes 2 and everything to the right of it
------
Answer: C)
Answer:
![\large \boxed{y = - \frac{1}{9} x - \frac{5}{9} }](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20-%20%20%5Cfrac%7B5%7D%7B9%7D%20%7D)
Step-by-step explanation:
In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.
![\large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7Bm%20%3D%20%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%7D)
m-term is defined as slope in y = mx+b form which is slope-intercept form.
Now we substitute these ordered pairs (x, y) in the formula.
![\large{m = \frac{1 - ( - 2)}{ -14 - 13} } \\ \large{m = \frac{1 + 2}{ - 27} } \\ \large{m = \frac{3}{ - 27} = - \frac{1}{9} }](https://tex.z-dn.net/?f=%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B1%20-%20%28%20-%202%29%7D%7B%20-14%20-%2013%7D%20%7D%20%5C%5C%20%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B1%20%2B%202%7D%7B%20-%2027%7D%20%7D%20%5C%5C%20%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B3%7D%7B%20-%2027%7D%20%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%7D)
After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is
![\large \boxed{y = mx + b}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7By%20%3D%20mx%20%2B%20b%7D)
We already know m-value as we substitute it.
![\large{y = - \frac{1}{9} x + b}](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20%20%2B%20b%7D)
We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)
We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.
![\large{y = - \frac{1}{9} x + b} \\ \large{ - 2 = - \frac{1}{9} (13) + b} \\ \large{ - 2 = - \frac{13}{9} + b} \\ \large{ - 2 + \frac{13}{9} = b} \\ \large{ - \frac{5}{9} = b}](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%202%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%2813%29%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%202%20%3D%20%20-%20%20%5Cfrac%7B13%7D%7B9%7D%20%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%202%20%2B%20%20%5Cfrac%7B13%7D%7B9%7D%20%20%3D%20b%7D%20%5C%5C%20%20%5Clarge%7B%20-%20%20%5Cfrac%7B5%7D%7B9%7D%20%20%3D%20b%7D)
Finally, we know b-value. Then we substitute it in our equation.
![\large{y = - \frac{1}{9} x + b} \\ \large{y = - \frac{1}{9} x - \frac{5}{9} }](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7By%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20x%20-%20%20%5Cfrac%7B5%7D%7B9%7D%20%7D)
Noooooooooooooooooooooooo