# Hotmath Practice Problems

Title:
Hotmath Precalculus
Author:
Hotmath Team
Chapter:Relations and FunctionsSection:Exercises

Problem: 1

State the domain and range of the relation. Then state whether the relation is a function. Write yes or no. Explain.

{(0, 0), (2, 2), (2, –2), (6, 8), (6, –8)}

Problem: 2

State the domain of the function

Problem: 3

Find the value of the constant a so that the graph of the equation passes through the point (–5, 2).

y = a(x – 6)2 – 2

Problem: 4

Find the equation in y = mx + b form for the line which has the same x– and y–intercepts as the circle x2 + y2 + 4x – 4y + 4 = 0

Problem: 5

Find

for the following f(x) and g(x) .

f(x) = x – 4 and g(x) = 3x2

Problem: 6

Consider the equation y = 4x2/(1+ x2). Use a calculator to set up a table of values running from x = 0 to x = 4, with 0.5 unit increments. Graph the equation using these points and symmetry.

Problem: 7

Determine whether the graphs of the pair of equations are parallel, coinciding, perpendicular, or none of these.

4x – 6y = 11

3x + 2y = 9

Problem: 8

Write the standard form of the equation of the line that is perpendicular to the graph of the equation y = 5x + 12 and passes through the point (0, –3).

Problem: 9

An altitude of a triangle is a segment that passes through one vertex and is perpendicular to the opposite side. Find the standard form of the equation of the line containing each altitude of ΔABC.

Problem: 10

Solve the inequality, and write the answer in interval notation.

Problem: 11

Solve the inequality, and write the answer in interval notation.

Problem: 12

Graph the function.

h(x) = [[x – 1 ]]

(Here [[ ]] indicates the greatest integer function.)

Problem: 13

Graph the function.

Problem: 14

Solve the inequality.

x2 – 8x + 2 0

Problem: 15

Find f(x) + g(x), f(x) –g(x), f(x) ·g(x), and

for the following f(x) and g(x) .

f(x) = x2 – 4x and g(x) = 4/(x – 4)

Problem: 16

Graph the data below on a scatter plot. Choose two ordered pairs and write the equation of a line of best fit. Use a graphing calculator to find an equation of the regression line for the data, and find the correlation value. Finally, if the regression line shows a moderate strong relationship, predict the number of visitors in 2005. Is this prediction reliable?

Problem: 17

The vertices of ΔABC are A(1, 1), B(9, 3), and C(3, 5). Find the perimeter of the triangle. Then find the perimeter of the triangle formed by joining the midpoints of the three sides. Find the ratio between the two perimeters. What property have you just verified?

Problem: 18

Given points S(4, 6) and T(10, 2) and M, the midpoint of find the midpoint of

Problem: 19

If f(x) = x/(x – 1), compute the difference quotient:

Problem: 20

Specify the domain and range of the function shown.

Problem: 21

Compute the average rate of change for the function f(x) = x2 + 2x on the interval [4, 6].

Problem: 22

If the graph shows the function f, graph the function f –1(x).

Problem: 23

If the graph shows the function g, graph the function y = g –1(x – 1).

Problem: 24

Which of the following expressions is not larger than 5 612?

A: 5 + 612

B: 7 612

C: 5 814

D: 5 614

E: 1013

Problem: 25

Suppose xy 0. Describe the points whose coordinates are solutions to the inequality.