I am refering to the question posted on Tuesday, June 6, 2017 at 8:26pm.

"how to graph y= (x^2-3x-10)/(x-2)"

This is the reply I got:

Pre-Calculus 12 - Damon, Tuesday, June 6, 2017 at 9:21pm
(x-5)(x+2)/(x-2)

well we know it is 0 at x = 5 and at x = -2
and we know it explodes at x = 2

we know it goes to y = x as x gets +big

we know it goes to y = -x as x gets -big

now between those zeros at -2 and+5
lies x = 0 when y is 10/2 = 5

so that is a start :)

My question is I don't understand what you mean "it is 0 at x=5 and at x=-2"? I haven't been taught how to graph these questions so please help!

y = (x-5)(x+2)/(x-2)

a fraction is zero when its numerator is zero, right?

Damon was just trying to give you the x-intercepts as an aid to graphing the curve.

With Damon's input, you have the x-intercepts, the asymptote, and the y-intercept.

Unfortunately, the asymptote is not y=x or y=-x. If you do the division, you see that

y = x-1 - 12/(x-2)

Now, as x gets huge, 12/(x-2) goes to zero, so the asymptote is the line

y = x-1

See the info at

http://www.wolframalpha.com/input/?i=(x-5)(x%2B2)%2F(x-2)

Are there specific steps to graphing this equation or do you just plot points?

well, you have to know the basic steps to finding intercepts and asymptotes.

Review the examples in your text, and then it's just a matter of figuring out the relevant features of the graph. The intercepts and stuff are just handy landmarks to pinpoint specific places.

I apologize for any confusion. When it is mentioned that the function is "0 at x = 5 and at x = -2", it means that when you substitute these values into the equation y = (x^2 - 3x - 10)/(x - 2), the result is zero.

To understand this concept, you can start by setting the numerator of the function, x^2 - 3x - 10, equal to zero and solving for x:

x^2 - 3x - 10 = 0

This is a quadratic equation that can be factored as (x - 5)(x + 2) = 0. This means that when x equals 5 or -2, the numerator of the function equals zero.

Next, consider what happens when the denominator, x - 2, equals zero:

x - 2 = 0

Solving this equation, we find that x = 2. However, it's important to note that this value is not included in the domain of the function because it would result in division by zero, which is undefined. Therefore, the function "explodes" or becomes undefined at x = 2.

Now, to understand the behavior of the function as x approaches positive infinity and negative infinity, you need to consider the leading terms of the equation. In this case, the leading terms are x^2 in the numerator and x in the denominator.

As x approaches positive infinity, the x^2 term in the numerator becomes dominant, and the function behaves like y = x^2/x = x. This means that the graph gradually approaches the line y = x as x gets larger and larger.

As x approaches negative infinity, the numerator's x^2 term is still dominant, but it becomes negative. So, the function behaves like y = -x^2/x = -x. This means that the graph gradually approaches the line y = -x as x moves toward negative infinity.

Finally, between x = -2 and x = 5, there is a point where the function has a y-value of y = 5. This point is found by substituting x = 0 into the equation (x^2 - 3x - 10)/(x - 2):

y = (0^2 - 3(0) - 10)/(0 - 2) = (-10)/(-2) = 5

So, the point (0, 5) is on the graph.

By understanding these key points and characteristics of the function, you can start sketching the graph of y = (x^2 - 3x - 10)/(x - 2).