Why algebraic functions

Worked example: determining domain word problem positive integers Opens a modal. Worked example: determining domain word problem all integers Opens a modal.

Determine the domain of functions. Function domain word problems. Recognizing functions. Recognizing functions from graph Opens a modal. Does a vertical line represent a function? Recognizing functions from table Opens a modal. Recognizing functions from verbal description Opens a modal. Recognizing functions from verbal description word problem Opens a modal. Recognize functions from graphs. Recognize functions from tables. Piecewise functions. Introduction to piecewise functions Opens a modal.

Worked example: evaluating piecewise functions Opens a modal. Worked example: graphing piecewise functions Opens a modal. Evaluate piecewise functions. Evaluate step functions. Piecewise functions graphs. Maximum and minimum points. Introduction to minimum and maximum points Opens a modal. Worked example: absolute and relative extrema Opens a modal. Relative maxima and minima.

Absolute maxima and minima. Intervals where a function is positive, negative, increasing, or decreasing. Increasing, decreasing, positive or negative intervals Opens a modal. Positive and negative intervals. Increasing and decreasing intervals. Interpreting features of graphs. Graph interpretation word problem: temperature Opens a modal. Graph interpretation word problem: basketball Opens a modal. Graph interpretation word problems. Average rate of change.

Introduction to average rate of change Opens a modal. Worked example: average rate of change from graph Opens a modal. Worked example: average rate of change from table Opens a modal. Worked example: average rate of change from equation Opens a modal.

Average rate of change of polynomials. Average rate of change word problems. Average rate of change word problem: table Opens a modal. Average rate of change word problem: graph Opens a modal. Average rate of change word problem: equation Opens a modal. Average rate of change review Opens a modal. Combining functions. Intro to combining functions Opens a modal. Adding functions Opens a modal. Subtracting functions Opens a modal. Adding and subtracting functions Opens a modal. Multiplying functions Opens a modal.

Dividing functions Opens a modal. Multiplying and dividing functions Opens a modal. Composing functions Algebra 2 level. Intro to composing functions Opens a modal. Composing functions Opens a modal. Any vertical line in the bottom graph passes through only once and hence passes the vertical line test, and thus represents a function.

If, alternatively, a vertical line intersects the graph no more than once, no matter where the vertical line is placed, then the graph is the graph of a function. For example, a curve which is any straight line other than a vertical line will be the graph of a function. Apply the vertical line test to determine which graphs represent functions.

Applying the Vertical Line Test: Which graphs represent functions? If any vertical line intersects a graph more than once, the relation represented by the graph is not a function. From this we can conclude that these two graphs represent functions. This is shown in the diagram below. Not a Function: The vertical line test demonstrates that a circle is not a function.

Privacy Policy. Skip to main content. Search for:. Introduction to Functions. Learning Objectives Connect the notation of functions to the notation of equations and understand the criteria for a valid function. Key Takeaways Key Points Functions are a relation between a set of inputs and a set of outputs with the property that each input maps to exactly one output. Typically functions are named with a single letter such as f.

Functions can be thought of as a machine in a box that is open on two ends. You put something into one end of the box, it somehow gets changed inside of the box, and then the result pops out the other end. Key Terms output : The output is the result or answer from a function. Learning Objectives Describe the relationship between graphs of equations and graphs of functions. Key Takeaways Key Points Functions have an independent variable and a dependent variable. As you choose any valid value for the independent variable, the dependent variable is determined by the function.

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