Search the California Content Standards

Cluster:
Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

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.

Cluster:
Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

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.

Cluster:
Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

Standard:
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^3 or f(x) = (x + 1)/(x − 1) for x ≠ 1.

Cluster:
Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

Standard:
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^3 or f(x) = (x + 1)/(x − 1) for x ≠ 1.

Cluster:
Use probability to evaluate outcomes of decisions. [Include more complex situations.]

Standard:
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *

Cluster:
Use probability to evaluate outcomes of decisions. [Include more complex situations.]

Standard:
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *

Cluster:
Use probability to evaluate outcomes of decisions. [Include more complex situations.]

Standard:
(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). *

Cluster:
Use probability to evaluate outcomes of decisions. [Include more complex situations.]

Standard:
(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). *

Cluster:
Calculate expected values and use them to solve problems.

Standard:
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. *

Cluster:
Calculate expected values and use them to solve problems.

Standard:
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. *