Answer:
![\boxed{ \text{Option \: D}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%20%5Ctext%7BOption%20%5C%3A%20D%7D%7D)
Step-by-step explanation:
All the relations are not functions. We can determine ( identify ) whether a relation is function or not by drawing a vertical line intersecting the graph of the relation. This is called vertical line test.
- If the vertical line intersects the graph of a relation at one point , the relation is a function .
- If it cuts at more than one point , it is not a function. It means that if there are more points of the graph of a relation of a vertical line , same first component ( pre - image ) has more images ( second component ) which is not the function by definition.
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Let's check all of the options :
☐ Option A :
- The vertical line cuts the graph at two points. So , the graph does not represent a function.
☐ Option B
- No! This is also not a function as the vertical line cuts the graph at two points.
☐ Option C
- Nah! This too can't be called a function as the vertical line cuts the graph at two points.
☑ Option D
- Yep! The vertical line cuts the graph at one point. Thus , the graph represents a function.
Yayy!! We found our answer. It's ' Option D '.
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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<u> 1 liter </u> = <u>12 km
</u>3 liters x km
<u>
</u>x= 12km x 3 liters ÷ 1 liter
<u />x= 36 km
But since we want to know how many METERS the car can travel, convert km to m:
<u> 1 km </u>= <u>1000m</u>
36 km y m
y= 1000 x 36m ÷ 1 km
y= 36000m
Hope this helps!
Given a piecewise function:
![f(x) = \left\{ \begin{array}{rcl} 3x-5} & \mbox{if} & x \leq-1 \\ -2x+3 & \mbox{if} & -1 < x < 4 \\ {2} & \mbox{if} &x \geq4 \end{array}\right.](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cleft%5C%7B%20%5Cbegin%7Barray%7D%7Brcl%7D%203x-5%7D%20%26%20%5Cmbox%7Bif%7D%20%26%20x%20%5Cleq-1%20%5C%5C%20-2x%2B3%20%26%20%5Cmbox%7Bif%7D%20%26%20-1%20%3C%20x%20%3C%204%20%5C%5C%20%7B2%7D%20%26%20%5Cmbox%7Bif%7D%20%26x%20%5Cgeq4%20%5Cend%7Barray%7D%5Cright.)
To graph the function follow the steps below:
<h3>Step 1</h3>
Graph the first function, f(x) = 3x - 5
Plot two points with x- coordinates - 1 and 0. We considered x ≤ -1 when selecting points.
- f(-1) = 3(-1) - 5 = - 8
- f(-2) = 3(-2) - 5 = - 11
Make point (- 1, - 8) a full dot and connect two points, then extend the line to the left from x = -2.
<h3>Step 2</h3>
Graph the second function, f(x) = - 2x + 3.
Plot both endpoints with x - coordinates of - 1 and 4.
- f(-1) = - 2(-1) + 3 = 5
- f(4) = - 2(4) + 3 = - 5
Make both points (-1, 5) and (4, 5) open dots and connect together.
<h3>Step 3</h3>
Graph the third function, f(x) = 2.
Every point of this function has the value of 2, we are interested in the endpoint when x = 4.
Make this point a full dot and make a line parallel to the x-axis, to the right from the plotted point.
Now we have the full graph, <u>see attached</u>.
Answer:
(- 1, 2 )
Step-by-step explanation:
Given the 2 equations
2x + 5y = 8 → (1)
- x + 3y = 7 → (2)
Multiplying (2) by 2 and adding to (1) will eliminate the term in x, thus
- 2x + 6y = 14 → (3)
Add (1) and (3) term by term to eliminate the x- term
11y = 22 ( divide both sides by 11 )
y = 2
Substitute y = 2 in either of the 2 equations and evaluate for x
Substituting in (1)
2x + 5(2) = 8
2x + 10 = 8 ( subtract 10 from both sides )
2x = - 2 ( divide both sides by 2 )
x = - 1
Solution is (- 1, 2 )