#### California Common Core State Standards for Mathematics

**Core Content Standards**

Coherence Map Domain 8.F Functions

8.F.A.3 Interpret the equation \(y = mx + b\) as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function \(A = s^2\) giving the area of a square as a function of its side length is not linear because its graph contains the points \((1,1)\), \((2,4)\)and \((3,9)\), which are not on a straight line. Use functions to model relationships between quantities.

8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two \((x, y)\) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

HSF.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.*

**Related Standards**

Analyze functions using different representations.

HSF.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.*

HSF.IF.C.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.

**Standards for Mathematical Practice **

SMP1: Make sense of problems and persevere in solving them.

SMP2: Reason abstractly and quantitatively.

SMP5: Use appropriate tools strategically.

SMP6: Attend to precision.

SMP7: Look for and make use of structure.

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