Search the California Content Standards

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:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. * Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. *

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

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 exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. *

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.

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 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, and y = (1.2)^t/10, and classify them as representing exponential growth or decay.

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

Standard:
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.

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:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), 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.