Question 1

can a horizontal line represent a function?

Accepted Answer

y = 5 is a horizontal line and is indeed a function.

Question 2

could he have just used the vertical line test?

Accepted Answer

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!

Question 3

Can there be many domain but getting only one range? If the line will be horizontal will it be a function?

Accepted Answer

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.

Question 4

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?

Accepted Answer

Infinity cannot be a single output. This rhetorical question I'm about to give you came from another user: "Think of the biggest, biggest, biggest number you can then keep adding 1." There is no definite answer for infinity, so it can't be considered as a single output.

Question 5

is a function with multiple outputs a logarithm?

Accepted Answer

No. A function, by definition, can not have multiple outs for a specific input value. Each input can create only one output to be a function. Thus, any equation that doesn't meet this definition would not be a function.

FYI.. there are logarithmic functions.

FYI.. there are logarithmic functions.

Question 6

Can a vertical line be represented by an equation?

Accepted Answer

Yes.  Points on a vertical line would all have the same X value, but could take on any value for Y.  So there would be no Y value in the equation.
For instance, if the vertical line crossed the X-axis at x=2, then x=2 would be its equation!

Question 7

does anyone know how to solve this? : 
"solve by graphing and check" y= -2x-2 and y=-4 ??

Accepted Answer

_*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.

_*Continued in Comments*_

Question 8

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?

Accepted Answer

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.

Question 9

What's the vertical and horizontal line test?

Accepted Answer

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.

Question 10

If we consider the following  function f(x) =x^2+2 
So if we input - 1 or 1 we will get 3 so my question is if two different inputs gives the same output will it be considered a function?

Accepted Answer

Yes, it will still be a function.
The restriction is that *one input* can not create *two outputs*.  
For example, if you have an equation where your can input 2, but the equation can create an output of 4 or -6, then it is not a function.  Functions are predictable.  One input will create one output.  It is perfectly ok for different inputs to create the same output.

Algebra 1

Course: Algebra 1 > Unit 8

Does a vertical line represent a function?

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