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Khan Academy Resources
Analyze vertical asymptotes of rational functions
Analyze vertical asymptotes of rational functions
Related Video
Sal analyzes the behavior of q(x)=(x²+3x+2)/(x+3) around its vertical asymptote at x=-3.
End behavior of rational functions
End behavior of rational functions
Related Video
Sal analyzes the end behavior of several rational functions, that together cover all cases types of end behavior.
Graph from slope-intercept form
Graph from slope-intercept form
Graph from linear standard form
Graph from linear standard form
Related Video
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.
Graphing linear relationships word problems
Graphing linear relationships word problems
Related Video
Sal is given a verbal description of a real-world relationship involving a truck's fuel consumption, and is asked to draw the graph that represents this relationship.
Complete solutions to 2-variable equations
Complete solutions to 2-variable equations
Related Video
Given a 2-variable equation and the x or y values of a solution, Sal finds the value of the other variable in the solution.
Graphs of rational functions
Graphs of rational functions
Related Video
Sal picks the graph that matches f(x)=(ax^m+bx+12)/(cx^m+dx+12) based on its y-intercept.
Increasing and decreasing intervals
Increasing and decreasing intervals
Related Video
Function values can be positive or negative, and they can increase or decrease as the input increases. Here we introduce these basic properties of functions.
Graph interpretation word problems
Graph interpretation word problems
Related Video
When a function models a real-world context, we can learn a lot about the content from the function's graph. In this video, we consider a graph that models temperature over time.
Linear equations word problems: graphs
Linear equations word problems: graphs
Related Video
Sal finds the y-intercept and the slope of a linear relationship representing someone accumulating cats! He then interprets what the y-intercept and the slope mean in that context.
Piecewise functions graphs
Piecewise functions graphs
Related Video
Functions assign outputs to inputs. Some functions have simple rules, like "for every x, return x²." However, there can be other rules that are more elaborate. For example, "If x<0, return 2x, and if x≥0, return 3x." These are called *piecewise functions*, because their rules aren't uniform, but consist of multiple pieces. A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1
Positive and negative intervals
Positive and negative intervals
Related Video
Finding the positive or negative intervals of a function from its graph.
Relative maxima and minima
Relative maxima and minima
Related Video
Extrema is the general name for maximum and minimum points. This video shows how to identify relative and absolute extrema in the graph of a function.
Intercepts from an equation
Intercepts from an equation
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