What a function is and how to read it from graphs, tables, and notation
Build the language, notation, and graph-reading skills needed to understand functions.
Common CoreF-IF.A.1F-IF.A.2F-IF.B.4F-IF.B.6
7 lessons25 short videos6 key concepts, out loud
4.1
Relations, Domain & Range
The inputs and outputs of a relation
F-IF.A.1
Key idea
The domain is the set of all possible inputs (x-values) and the range is the set of all possible outputs (y-values) of a relation.
Learn how to identify inputs and outputs, and find the domain and range of relations from lists and graphs.
Key concept · Lesson 4.1
Inputs in, outputs out
Listen0:00 / 0:21
Transcript. A relation pairs inputs with outputs. The domain collects every input, the x values, and the range collects every output, the y values. Read a table down the first column for the domain and the second for the range, and list each value only once.
4.2
Function Notation f(x) vs. y
Learn how to use f(x) instead of y to show inputs and outputs
F-IF.A.2
Key idea
Function notation f(x) represents the output (y-value) of a function named f when the input is x, showing how the input and output are connected.
Learn how to read and write function notation, evaluate functions for given inputs, and find inputs that produce given outputs.
Key concept · Lesson 4.2
Plug in the input
Listen0:00 / 0:23
Transcript. Function notation renames the output. Instead of writing y, we write f of x, which says: here is the rule named f, and here is the input it received. So f of three means replace every x with three and simplify. It is a name, never multiplication.
4.3
The Vertical Line Test
Decide whether a graph is a function
F-IF.A.1
Key idea
A graph represents a function if and only if no vertical line intersects it more than once, meaning each input has exactly one output.
Learn how to use a vertical line to visually check if a graph represents a function.
Key concept · Lesson 4.3
One output per input
Listen0:00 / 0:21
Transcript. A function gives each input exactly one output. To test a graph, imagine sliding a vertical line across it. If that line ever touches the graph in two places at once, one input has two outputs and the graph is not a function. Repeated outputs are fine.
4.4
Evaluating & Interpreting Functions
Input numbers into a function and read function values from a graph
F-IF.A.2
Key idea
Evaluating a function means finding the output that corresponds to a specific input using an equation, a graph, or a real-world scenario.
Learn how to find function outputs from equations and graphs, and interpret what those values mean in real-world scenarios.
Key concept · Lesson 4.4
Substitute, then simplify
Listen0:00 / 0:20
Transcript. Evaluating means replacing every x with the given input, then simplifying. Wrap a negative input in its own parentheses, or the square will lose its sign. On a graph, find the input along the bottom axis first, then read the height of the curve above it.
4.5
Key Features of Graphs
Find intercepts, peaks, valleys, and where a graph goes up or down
F-IF.B.4
Key idea
To analyze a graph, identify where it crosses the axes (intercepts), its highest and lowest points (extremes), and the intervals of x-values where it goes up or down.
Learn how to read a graph to find where it reaches its highest and lowest points, crosses the axes, and goes up or down.
Key concept · Lesson 4.5
Read a graph in three passes
Listen0:00 / 0:23
Transcript. Read a graph in three passes. First the intercepts: where it crosses the bottom axis and the side axis. Then the extremes: the highest and lowest turning points. Finally the intervals where it rises or falls, always described using x values, never y values.
4.6
Average Rate of Change
How fast a function changes over an interval
F-IF.B.6
Key idea
The average rate of change is simply the slope of the straight line connecting two points on a curve.
Learn how to calculate and interpret the average speed of a function between two points on its graph.
Key concept · Lesson 4.6
Slope between two points
Listen0:00 / 0:21
Transcript. Average rate of change is the slope of the straight line joining two points on the curve. Square brackets show an input interval, not a coordinate point: the first number is the starting input, and the second is the ending input. Find both outputs, subtract in the same order, and divide.
4.7
Review & Assessment
Notation, evaluation, and reading graphs
Review, practice, quiz and test
Key idea
Review notation, evaluation, and graph reading with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
