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Question 1

Suppose the algebraic rule for a linear function is given in the form: y = 2x – 4.

Describe how this function compares to the linear parent function.

You could talk about slope, the shapes of each graph, or any characteristics that these functions have or do not have in common.

Question 2

Consider the graphs of all linear functions having the same slope.
What do they have in common and what might be different?

How are these similarities and differences reflected in the algebraic rules?

How might the similarities and differences be reflected in the real-world situations the functions represent?

Make a generalization about the graphs of all linear functions having the same slope.

Question 3

Consider the graphs of all linear functions having the same y-intercept.

What do they have in common and what might be different?

How are these similarities and differences reflected in the algebraic rules?

How might the similarities and differences be reflected in the real-world situations the functions represent?

Make a generalization about the graphs of all linear functions having the same y-intercept.

Question 4

Think of an example of a real-world situation that might be represented by a linear function. Print a Four-Corner Model, if you wish, to organize your thinking.

Describe the situation in words.

Write an algebraic rule for the situation in the form y = mx + b.

Describe the meaning of the particular values of m and b for this situation.

Write the same algebraic rule using the standard function notation (f of x notation).

Describe the graph of the function.

Find f(36). Describe its meaning in the context of your problem situation.