2. Modeling with Linear Functions, Linear Systems, & Exponential Functions

2.01 Graphing systems of equations

2.02 Solving systems of equations with the substitution method

2.03 Solving systems of equations with the elimination method

2.04 Solving systems of equations with a variety of methods

2.05 Applications of linear systems

2.06 Graphing linear inequalities in two variables

2.07 Systems of inequalities

2.08 Functions and relations

2.09 Domain and range and set notation

2.10 Evaluating functions

2.11 Modeling linear relationships

2.12 Review: Laws of exponents

2.13 Exponential growth and decay

Investigation: Comparisons of simple and compound interest

2.15 Compound interest

2.16 The slope formula

2.17 Transformations of y=x

Investigation: Exploring slopes and equations of lines

Investigation: Relationship between shoulder span and height

2.18 Slope-intercept form

2.19 Standard form

2.20 Point-slope form

2.21 Comparing linear relationships

2.22 Comparing exponential relationships

2.23 Comparing linear and exponential relationships

2.24 Review: Slope as rate of change

2.25 Key features of quadratic functions

2.26 Graphing quadratic functions

2.27 Quadratic functions and technology

2.28 Extension: Absolute value equations

2.29 Extension: Absolute value inequalities

2.30 Graphs and characteristics of absolute value functions

United States of America NJ

Algebra 1

2.17 Transformations of y=x

Interactive practice questions

On which of the following graphs is the linear function $decreasing$ ?

Loading Graph...

A

Loading Graph...

B

Easy

< 1min

The lines $y=x+2$y=x+2 (black line) and $y=x$y=x (gray line) have been graphed on the same set of axes.

Easy

< 1min

Consider the graph of $y=-4x$y=−4x.

Easy

< 1min

Consider the graph of $y=x-4$y=x−4.

Easy

1min

Outcomes

F.IF.B.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.

F.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.A

Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k*f(x), f(k*x), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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