# Hotmath Practice Problems

Title:
Hotmath Algebra 1
Author:
Hotmath Team
Chapter:Relations and FunctionsSection:Definitions: Relations and Functions

Problem: 1

Draw a mapping diagram and a graph of the following relation.

{(6, 1), (3, 1), (6, –5), (2, 7), (–8, 3)}

Problem: 3

Draw a mapping diagram and a graph of the following relation.

{(5, 0), (5, –2), (2, –1), (4, –1)}

Problem: 5

For the given relation, find the domain and range. Determine whether the relation is a function.

{(a, e), (c, b), (a,d)}

Problem: 7

For the given relation, find the domain and range. Determine whether the relation is a function.

Problem: 9

Is the relation a function? If so, give the domain and the range.

Problem: 11

Is the relation a function? If so, give the domain and the range.

Problem: 13

Is the relation a function? If so, give the domain and the range.

Problem: 15

Check whether the relation is a function. If yes, then give the domain and range.

Problem: 17

Check whether the relation is a function. If yes, then give the domain and range.

Problem: 19

Check whether the relation is a function. If yes, then give the domain and range.

Problem: 21

Does the graph represent y as a function of x? Explain.

Problem: 23

Does the graph represent y as a function of x? Explain.

Problem: 25

Check whether the graph represents a function. Explain your reasoning.

Problem: 27

Check whether the graph in the figure represents a function. Explain your reasoning.

Problem: 29

Check whether the graph in the figure represents a function. Explain your reasoning.

Problem: 31

Check whether the graph in the figure represents a function. Explain your reasoning.

Problem: 33

Check whether the graph in the figure represents a function. Explain your reasoning.

Problem: 35

The relation y = –3x is a set of ordered pairs (x, y) that satisfy the equation y = –3x. Identify whether this relation is a function.

Problem: 37

The relation x = |y| – 3 is a set of ordered pairs (x, y) that satisfy the equation x = |y| – 3. Identify whether this relation is a function.

Problem: 39

Find f(2),f(6), and f(–8) for the given function machine.

Problem: 41

Find h(–1),h(7), and h(12) for the given function machine.

Problem: 43

Evaluate the function at the given points.

h(y) = |y|, find h(–3),h(3), and h(–1).

Problem: 45

Find the indicated function values.

f(x) = |x| – 4, find f(4),f(90), and f(–151).

Problem: 47

Find the indicated function values.

h(x) = x3 – 12, find h(1), h(–2), and h(4).

Problem: 49

Find the value of f(–2) if f(x) = 5x + 3.

Problem: 51

Find the value of g(1/3) if g(x) = x2 – 5x.

Problem: 53

Find the value of g(2.5) if g(x) = x2 – 5x.

Problem: 55

Find the value of 4[ f(–3)] if f(x) = 5x + 3.

Problem: 57

Find the value of g(2b) if g(x) = x2 – 5x.

Problem: 59

Find the value of –4[g(2)] if g(x) = x2 – 5x.

Problem: 61

Find the value of 4[ g(a2)] if g(x) = x2 – 5x.

Problem: 63

A large tank is filled with a certain liquid. The function

gives the pressure in atmospheres of the liquid as a function of d in feet.

Find the pressure exerted on a object submerged (a) 20 feet, (b) 30 feet, (c) 50 feet in the tank.