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3 years ago

Graph the function and find the range

Mathematics

1 answer:

kramer3 years ago

6 0

The answer for the graph would be C. While x is less than or equal to 0, there is the graph of -4x. While x is greater than x, there is the graph of -5 (horizontal line). Furthermore, the closed dot at the end of the -4x represents the less than or EQUAL TO. The dot at the end of the -5 is open because it is only true when x > 0.

The range (y-values where the graph exists) is [-5]∪[0, infinity)

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Use the order pairs to write a function rule. Give the tule in slope-intercept form.

topjm [15]

to get the equation of any straight line, we simply need two points off of it, so hmmm let's use say (-1 , -1.25) and (8 , -3.5)

$(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1.25})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3.5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3.5}-\stackrel{y1}{(-1.25)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-1)}}}\implies \cfrac{-3.5+1.25}{8+1}\implies \cfrac{-2.25}{9}\implies -\cfrac{~~ \frac{225}{100}~~}{\frac{9}{1}} \\\\\\ -\cfrac{225}{100}\cdot \cfrac{1}{9}\implies -\cfrac{9}{4}\cdot \cfrac{1}{9}\implies -\cfrac{1}{4}$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1.25)}=\stackrel{m}{-\cfrac{1}{4}}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+1.25=-\cfrac{1}{4}(x+1)\implies y+\cfrac{5}{4}=-\cfrac{1}{4}x-\cfrac{1}{4} \\\\\\ y=-\cfrac{1}{4}x-\cfrac{1}{4}-\cfrac{5}{4}\implies y=-\cfrac{1}{4}x-\cfrac{6}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{2}$

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2 years ago

Solve each system of equations by substitution. <br> 2x + 2y = 3 x - 4y = -1

Shtirlitz [24]

Step-by-step explanation:

2x + 2y = 3 ( x2 for everything in the equation)

x - 4y = -1

4x+ 4y = 6

x - 4y = -1

Add the 1st line to the 2nd line to get rid of the y:

5x = 5

x - 4y = -1 ( you can pick any line from this system to be the second equation in this step, you can put 2x + 2y = 3 or 4x+ 4y = 6, anything above this step, but to make it simple chose the one you think is the easiest)

Solve for x, then plug the x value into the 2nd equation

x = 1

1 - 4y = -1

x = 1

-4y = -2 =) y = 1/2

x = 1

y= 1/2

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