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# Does a vertical line represent a function?

Explaining why a vertical line doesn't represent a function. Created by Sal Khan.

## Want to join the conversation?

• could he have just used the vertical line test? •  Yes, he could've. If he did that, then he would've noticed that the relation intersects the vertical line x=-2 at infinitely many points. This is because the relation is x=-2, so obviously it intersects it at infinitely many points.

However, I think Sal was trying to demonstrate a more rigorous way of testing a relation for being a function. Instead of just doing a vague, vertical line test, he used the definition of a function to test the relation for being a function.

I hope this helps!
• can a horizontal line represent a function? • Can there be many domain but getting only one range? If the line will be horizontal will it be a function? • One domain and one range although the domain can consist of the union of various regions on the x-axis. EG {-100 < x < -10} U {-1 < x < 1} U {10 < x < 100}. the U is the symbol of union.
A horizontal line is a function, but a pretty boring one since no matter what x value you input, the output will always be the same. EG f(x)=5. No matter what x is, the output is always 5. As you can see, the output value does not depend on the input value x.
• So is Sal saying that x -> f(x) -> infinity is not a function? If you just wrote the infinity sign could it be considered as only one output? • is a function with multiple outputs a logarithm? • Would a drastically curved line on a graph represent a function? Does the curve have to go through x and y to be a function?
(1 vote) • For a relation to be a function, use the Vertical Line Test: Draw a vertical line anywhere on the graph, and if it never hits the graph more than once, it is a function. If your vertical line hits twice or more, it's not a function. For example, a circle is not a function because when you draw a vertical line on top of its graph, the vertical line will cut through the circle twice.
• What's the vertical and horizontal line test?
(1 vote) • The vertical line test is used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function. This is based on the fact that a vertical line is a constant value of x, so if there is one input, x, with more than two outputs, y, then it breaks the function rule. A horizontal line test does not have as much meaning.
• Can a vertical line be represented by an equation? • does anyone know how to solve this? :
"solve by graphing and check" y= -2x-2 and y=-4 ?? • Graph to solve: y = -2x -2 and y = -4

y = -2x -2

Is in Slope Intercept Form, which means we can look at the equation and see the slope of the line is -2, (because it's the coefficient of x), the second term is the y intercept and also -2, (where the line crosses the y-axis).

y-intercept of -2, means…
when x is zero, y is -2.
So we're able to graph that Point.
Point at: (0, -2) ←y intercept

★ Since the Slope is Negative, -2, we know the line is decreasing, meaning it goes ↘️ downward from left to right, and…

•A Slope of -2, means every time we move one unit Right, we move two Down.

★So let's do that from the y intercept!
If we're at (0, -2) and need to…

move one to the Right,
that's plus one on x axis…
x = 0 + 1 = 1

and for y we need two Down,
that's minus 2 on y axis…
y = -2 -2 = -4

Now we have another coordinate on the same line!
Point at: (1, -4)

★(0, -2) and (1, -4)
Draw a line through both coordinate Points, to finish graphing the first equation.

• Now to graph…
y = -4
Notice there is no written slope in this equation, just a y intercept, this is because it's a…
↔️ a Horizontal Line, slope = 0
It runs flat crossing y-axis at -4.
Find -4 on y-axis, draw a straight, side to side, ↔️ Horizontal Line through it.

Look to see where these two lines cross.
That (x, y) coordinate is the Point of Intersection between these two lines, the only x and y coordinate pair that make both of these equations True Statements. 