IA1.AT.D.16: Analyze how changes to a function’s input or output affect the graph and its meaning in context. a. Identify how replacing f(x) with f(x + k) and f(x) + k changes the graph of a linear, exponential, or absolute value function. Describe the direction of the change and determine the value of k when given a graph. b. Explain how changing the input or output of a function affects the quantities represented in context. Use the structure and features of the parent function to justify how these changes impact the initial context.

Analyze how changes to a function’s input or output affect the graph and its meaning in context. a. Identify how replacing f(x) with f(x + k) and f(x) + k changes the graph of a linear, exponential, or absolute value function. Describe the direction of the change and determine the value of k when given a graph. b. Explain how changing the input or output of a function affects the quantities represented in context. Use the structure and features of the parent function to justify how these changes impact the initial context.

Example Problems
The graph of is shifted to the left by 5 units.

What is the equation of the new graph?
The graph of is reflected across the y-axis only.

What is the equation of the new graph?
The graph of is shifted up by 8 units.
What is the equation of the new graph?
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