Solutions

Problem Set 4

Functions

1. For each function below, determine the value stated

a) f(x) = x² for x<3 and x+7 otherwise. What is f(4)? f(0)? f(f(0))?

f(4) = 11 f(0) = 0 f(f(0)) = f(0) = 0

b) f(x) = x if x≥3 and 3 otherwise. What is f(3)? f(10)? f(0)? f(-3)?

f(3) = 3 f(10) = 10 f(0) = 3 f(-3) = 3

c) f(y) = 1 if y≥2 and 2 if y < 2. What is f(2)? f(0)?

f(2) = 1 f(0) = 2

d) f(x) = 1 if x is an integer and 2 otherwise. What is f(3)? f(2.2)? f(π)? f(1/2)?

f(3) = 1 f(2.2) = 2 f(pi) = 2 f(1/2) = 2

2. if f(x) = x² + 1 when x>1 and -x +3 for all other x, what is the graph of f?

3. if f(x) = x² for x > 3 and 2x + b for all other x, what value of b would cause the graph to be unbroken for all x?

b = 3