## Standards derived from the same national standard

Identify the effect on the graph of replacing π§(πΉ) by π§(πΉ) + π¬, π¬ π§(πΉ), π§(π¬πΉ), and π§(πΉ + π¬) for specific values of π¬ (both positive and negative); find the value of π¬ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Identify the effect on the graph of π(π₯) (linear, exponential, quadratic) replaced with π(π₯) + π, ππ(π₯), π(ππ₯), and π(π + π₯) for specific values of π (both positive and negative); find the value of π given the graphs. Experiment with contrasting cases and illustrate an explanation of the effects on the graph using technology.

Transform parent functions (π(π₯)) by replacing π(π₯) with π(π₯) + π, ππ(π₯), π(ππ₯), and π(π₯ + π) for specific values of π (both positive and negative); find the value of π 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.

Identify the effect on the graph of replacing π§(πΉ) by π§(πΉ) + π¬, π¬ π§(πΉ), π§(π¬πΉ), and π§(πΉ + π¬) for specific values of π¬ (both positive and negative); find the value of π¬ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Identify the effect on the graph of replacing π§(πΉ) by π§(πΉ) + π¬, π¬ π§(πΉ), π§(π¬πΉ), and π§(πΉ + π¬) for specific values of π¬ (both positive and negative); find the value of π¬ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Describe the effect of the transformations kf(x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph.

Identify the effect on the graph of replacing π(π₯) by π(π₯) + π, ππ(π₯), π(ππ₯), and π(π₯ + π) for specific values of π (both positive and negative); find the value of π 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.