5-2: Piecewise-Defined Functions

From the definition of absolute value,

3 |x| = (a)   when x ≥ 0.

From the definition of absolute value,

3 |x| = (a)   when x < 0.

Use the graph shown of f(x) =

x + 3, x < −1

−4x − 2, x ≥ −1

Over what part of the domain is function f decreasing?

• x < −1

• x ≥ 2

• x ≥ −1

• x < 2

Use the graph shown of f(x) =

x + 3, x < −1

−4x − 2, x ≥ −1

Over what part of the domain is function f increasing?

• x < −1

• x ≥ 2

• x ≥ −1

• x < 2

How are the pieces of a​ piecewise-defined function related to the​ domain? Explain.

• The intervals that are the domains of the pieces make up half the domain of the piecewise function with no overlap.

• The intervals that are the domains of the pieces make up half the domain of the piecewise function with 1 real number overlapping.

• The intervals that are the domains of the pieces make up the entire domain of the piecewise function with 1 real number overlapping.

• The intervals that are the domains of the pieces make up the entire domain of the piecewise function with no overlap.

For a given​ piecewise-defined function, the pieces of the function are defined for intervals of the​ domain, x≤−1 and x>−1.

Explain how you could find the​ y-intercept for the function over the intervals x≤−1 and x>−1​?

The​ y-intercept is included in the piece of the function that crosses the​ ​ (a)   The piece for the interval ​ (b)  

• y-axis
• x-axis
• x>-1
• x≤-1

Graph the​ piecewise-defined function.

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Write a piecewise function for the graph given.

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For the piecewise linear​ function, find ​​ f(−3​).

(a)  

For the piecewise linear​ function, find ​ f(−1​).

(a)