Piecewise Defined Functions

Write a piecewise function for the graph given.

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

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

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

Which piecewise function corresponds to this graph? (Take your time)

• f(x) = { x  if x < 4;   -x+1  if x ≥ 4

• f(x) = { x  if x ≤ 4;  -x+1  if x > 4

• f(x) = { -x+1  if x < 4;  x  if x ≥ 4

• f(x) = { -x+1  if x ≤ 4;  x if x > 4

How much does he earn for a 70 hour week?

• $1020

• $1140

• $840

• He works for free!

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