"Our graph, finalizing this, says, 'yep, it's a square root, but I reflected this way. I'm still gonna graph my square root function, that's about how that graph looks, that's at least a good sketch of it."
"So let's plug in 2 for x. It's going to be 1 over -1, which is -1. So we have the point (2, -1), which means that it's below the horizontal asymptote."
"If the 1.9 is not on your x-axis, it'll give you an error message."
"This gives you a lot more options to graph things or do all kinds of statistical analysis than a utility could ever do."
"Draw a very smooth curve throughout all the points is considered as a good graph."
"It's just a nice easy point to remember with these exponential graphs."
"We want to be able to solve equations graphically because there's no point in wasting our time doing an analytical technique when we don't have to."
"By just understanding the basic shapes of these graphs, we're going to be able to draw lots of complex things just by doing a little shifting."
"We're going to need to break this problem up into two separate problems because it really is the areas of one graph and then the rest of it is the area of another graph."
"Being able to graph lines is a huge part of algebra."
"The most common graph in ABA is a line graph."
"The slope of the line is immediately apparent, and the Y intercept is also apparent."
"Remember how to graph these: the first step is to factor the numerator and denominator as much as you can."
"The roots are where the graph crosses the x-axis."
"The y-intercept is where the graph cuts the y-axis, and the gradient allows you to graph this line straight away."
"If you really want to check how much, how many graphs you can draw, you're going to be using a library called Plotly."
"In this lesson, we are going to take a very detailed in-depth look at the graph of polar equations."
"One of the prettiest curves you will make when making your polar graphs."
"Vertex form of a parabola... is easy to graph, and we've done it many times before."
"The first thing you want to do when you're graphing is you want to find a nice balance."
"If you can factor and you know your zeros, your x-intercepts, you have a very clear graph with almost no work."
"Use that and end behavior and you have a very powerful graph."
"With these two things, multiplicity and end behavior, you have a very powerful graph."
"If you can turn your physics problem into a graph or a picture, do it."
"The degree of this polynomial is one bump, two bumps, three bumps, four bumps or four because it's three bumps plus one."
"Please comment and happy graphing."
"We're going to use that with our shifting to get a really good picture of our graph."
"That creates this place where I can use my key points to illustrate a shifting of this original three to the x graph."
"You can graph anything, any function of X."
"You can put multiple graphs on the plot at once and make them different colors to help distinguish them."
"Every time we draw any kind of graph, we always start off with some kind of heading."
"It's always nice to see this in a graph so that you have a really strong feeling that what you've done is correct and that this is the right way to go."
"The important part is that it looks similar to how an X cubed graph should look and we're really accurate with going through those coordinates."
"The really important point is that it's a nice curve and it goes through each of these points perfectly."
"When it comes to drawing a quadratic graph, we have a couple of methods that we can use."
"The equation of a straight line is always written in the form y equals mx plus c, where m is the gradient and c is the y-intercept."
"The graph of a logarithm looks like y equals log base a of our variable x."
"If we have a graph and we can identify some x-intercepts, well then we can build a function from it."
"Model the height of a rider as a sinusoidal function and graph one revolution."
"When you see a flat line, it just means that time is passing but her height above the ground is not changing."
"It will give you how high you go above the x-axis and how low you go in terms of absolute value."
"The x-intercepts of the graph of the function correspond to the zeros of the corresponding equation."
"The graph of y equals x squared is reflected in the line with equation y equals x to give the curve C."
"The most commonly efficient way to solve an equation in a calculator is by graphing using the x-intercept method."
"The graph of this \( x^2 \) curve looks something like that, this is the \( f(x) = x^2 \) curve."
"Pick the base function that's closest to what your graph looks like."
"If you look, this is a very symmetrical graph."
"The discriminant can also be very useful whenever we're sketching quadratic graphs."
"That's the y-intercept, right, and a positive slope. Boom, done."
"When we draw a line, we always want it in the form y equals mx plus c."
"When we are talking about the market, the first thing that we need to understand is how we graph the market."
"Graphing polynomials is like creating a roadmap for understanding the twists and turns of functions."
"If you know the original function and you know its graph, you can immediately draw the graph of the inverse."
"Line Y equals X, it looks like this, going through all of the coordinates that are 1, 1, 2, 2, 3, 3, 4, 4."
"Graphing absolute value functions using transformations."
"Use your graph to find estimates of the solutions."
"As I get infinitely smaller, I go to the left, and I look at a graph or table and say, 'What was happening as I go to the right?'"
"You'll understand how to plot or graph an ordered pair, how to connect the dots in the XY or the coordinate plane."
"The most important point that you want to find when graphing the parabola is the vertex."
"In sketching the demand and supply functions, you need to work with the intercepts."
"When we talked about a function in single variable calculus, the graph of that function was some kind of one-dimensional curve in the x-y plane."
"On a graph, f prime of a is equal to the slope of the tangent line and it represents the instantaneous rate of change."
"It is appropriate to draw a line through the points because there is a constant rate of change."
"Given the graph of a function, be able to write its equation."
"Let's go ahead and say that the title of this plot here is multiple plots using the show command."
"This is lesson six, and here, this is what we're doing today: lesson six, plot anything."
"That's the graph of the oblique asymptote, ladies and gentlemen, done and done."
"Our slope of our graph if we want it to be G or the acceleration a should be 2 H over T squared."
"Quadratics are these functions that when you graph them, it gives you a parabola."
"We move now left by 2 and up by 5."
"This now is the completed square form and this is what happens to the graph as a result."
"When you graph them you will have the exact same graph showing you that they are equivalent."
"You will get, as different as these equations look, the exact same graph."
"It's fantastic as well if you want to try and whip some trig functions and graph them and solve equations, it really is quite interesting."