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

3.14159, he actually started defining pi :)

Accepted Answer

yes I saw that to. :)

Question 5

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 6

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 7

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 8

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 9

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 10

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.

Algebra 1

Course: Algebra 1 > Unit 8

Does a vertical line represent a function?

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