Search the California Content Standards

Cluster:
Analyze functions using different representations. [Linear and exponential]

Standard:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Cluster:
Extend the properties of exponents to rational exponents.

Standard:
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5(^1/3)^3 to hold, so (5^1/3)^3 must equal 5.

Cluster:
Extend the properties of exponents to rational exponents.

Standard:
Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Cluster:
Use properties of rational and irrational numbers.

Standard:
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

Standard:
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. *

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

Standard:
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. *

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. * Graph linear and quadratic functions and show intercepts, maxima, and minima. *

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. * Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. *

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 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.