Problems

For each of the following functions (Problems 1-8), make a table showing the value of f(x) when x = -1, -½, 0, ½, 1. Put a * where f(x) is undefined. Example:

1          f(x) = x/3 

2          f(x)=3

3          f(x) = 3x³ - 5x² + 2

4          f(x) = 1/(x - 1)

5          f(x)=

6          f(x) = |x|

7          f(x) = |x-½| + |x + ½|

8          f(x) =

9           Is the set of ordered pairs {(3, 2), (0, 1), (4, 2)} a function ?

10           Is the set of ordered pairs {(0, 2), (3, 6), (3, 4)} a function ?

11           If f is the function f(x) = 1 + x + x², find f(2), f(t), f(t + Δt), f(1 + t + t²), f(g(t)).

12           If f(x) = 1/x, find f(t), f(t + Δt), f(t²), f(1/t), f(g(0).

13           If f(x) = x, find f(t), f(t + Δt), f(t²),f(√t), f(g(t)).

14          If f(x) = ax + b, find f(ct + d), f(t²), f(1/t), f(t/a), f(g(t)).

For each of the following functions (Problems 15-20), find f(x + Δx) - f(x).

15          f(x) = 4x + 1

16         f(x) = x² - x

17         f(x) = x^-2 

18         f(x) = x⁴

19         f(x) = √x 

20         f(x) = 4

21            Find the domain of the function f(x) = 1/(x² — 1).

22            Find the domain of the function f(z) =

23            What is the domain of the function f(x) = √x?

24            What is the domain of the function f(t) =?

25            What is the domain of the function f(x) = 1/?

26            Show that if a and b have the same sign then |a + b| = |a| + |b|, and if a and b have opposite signs then |a + b| < |a| + |b|.