Graphing Lines Practice
Plot points, create lines, find the slope of a line.
Then, students will manipulate the slope of the line to see how changing the points changes the slope of the line greatly.
2 Direct Instruction
Graph a line with intercepts, points, or naming a function.
It will also show a table and you can change the scales of the graphs.
3 Guided Practice
Students will be given 4 different graphs. They have to figure out the story behind what the function represents.
4 Independent Practice
Manipulate linear functions and slide the slope and intercepts to see how it changes a line.
The app will give students a line. They have to guess correct points and the equation of a line in a game format.
Key Standards Supported
|HSF.IF: Analyze Functions Using Different Representations|
|HSF.IF.7||Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★|
|HSF.IF.7.a||Graph linear and quadratic functions and show intercepts, maxima, and minima.|
|HSF.IF.7.b||Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.|
|HSF.IF.7.c||Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.|
|HSF.IF.7.d||(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.|
|HSF.IF.7.e||Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.|
|HSF.IF.8||Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.|
|HSF.IF.8.a||Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.|
|HSF.IF.8.b||Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.|
|HSF.IF.9||Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.|
|Interpret Functions That Arise In Applications In Terms Of The Context|
|HSF.IF.4||For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★|
|HSF.IF.5||Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★|
|HSF.IF.6||Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★|
|Understand The Concept Of A Function And Use Function Notation|
|HSF.IF.1||Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).|
|HSF.IF.2||Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.|
|HSF.IF.3||Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.|
Linear, Quadratic, And Exponential Models
|HSF.LE: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems|
|HSF.LE.1||Distinguish between situations that can be modeled with linear functions and with exponential functions.|
|HSF.LE.1.a||Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.|
|HSF.LE.1.b||Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.|
|HSF.LE.1.c||Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.|
|HSF.LE.2||Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).|
|HSF.LE.3||Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.|
|HSF.LE.4||For exponential models, express as a logarithm the solution to abct =dwherea,c,anddarenumbersandthebasebis2,10,ore; evaluate the logarithm using technology.|
|Interpret Expressions For Functions In Terms Of The Situation They Model|
|HSF.LE.5||Interpret the parameters in a linear or exponential function in terms of a context.|