Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo

Practice Test

447.

For the functions, f(x)=6x+1f(x)=6x+1 and g(x)=8x3,g(x)=8x3, find (fg)(x),(fg)(x), (gf)(x),(gf)(x), and (f·g)(x).(f·g)(x).

448.

Determine if the following set of ordered pairs represents a function and if so, is the function one-to-one. {(−2,2),(−1,−3),(0,1),(1,−2),(2,−3)}{(−2,2),(−1,−3),(0,1),(1,−2),(2,−3)}

449.

Determine whether each graph is the graph of a function and if so, is it one-to-one.


This figure shows a parabola opening to the right with vertex (negative 3, 0).



This figure shows an exponential line passing through the points (negative 1, 1 over 2), (0, 1), and (1, 2).
450.

Graph, on the same coordinate system, the inverse of the one-to-one function shown.

This figure shows a line segment passing from the point (negative 3, 3) to (negative 1, 2) to (0, negative 2) to (2, negative 4).
451.

Find the inverse of the function f(x)=x59.f(x)=x59.

452.

Graph the function g(x)=2x3.g(x)=2x3.

453.

Solve the equation 22x4=64.22x4=64.

454.

Solve the equation ex2e4=e3x.ex2e4=e3x.

455.

Megan invested $21,000$21,000 in a savings account. If the interest rate is 5%,5%, how much will be in the account in 8 years by each method of compounding?
compound quarterly
compound monthly
compound continuously.

456.

Convert the equation from exponential to logarithmic form: 10−2=1100.10−2=1100.

457.

Convert the equation from logarithmic equation to exponential form: 3=log73433=log7343

458.

Solve for x: log5x=−3log5x=−3

459.

Evaluate log111.log111.

460.

Evaluate log4164.log4164.

461.

Graph the function
y=log3x.y=log3x.

462.

Solve for x:
log(x239)=1log(x239)=1

463.

What is the decibel level of a small fan with intensity 10−810−8 watts per square inch?

464.

Evaluate each. 6log6176log617
log99−3log99−3

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible.

465.

log 5 25 a b log 5 25 a b

466.

ln e 12 8 ln e 12 8

467.

log 2 5 x 3 16 y 2 z 7 4 log 2 5 x 3 16 y 2 z 7 4

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.

468.

5 log 4 x + 3 log 4 y 5 log 4 x + 3 log 4 y

469.

1 6 log x 3 log ( x + 5 ) 1 6 log x 3 log ( x + 5 )

470.

Rounding to three decimal places, approximate log473.log473.

471.

Solve for x:
log7(x+2)+log7(x3)=log724log7(x+2)+log7(x3)=log724

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

472.

( 1 5 ) x = 9 ( 1 5 ) x = 9

473.

5 e x 4 = 40 5 e x 4 = 40

474.

Jacob invests $14,000 in an account that compounds interest quarterly and earns 4%.4%. How long will it take for his money to double?

475.

Researchers recorded that a certain bacteria population grew from 500 to 700 in 5 hours. At this rate of growth, how many bacteria will there be in 20 hours?

476.

A certain beetle population can double in 3 months (A=2A0).(A=2A0). How long will it take for that beetle population to triple?

Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
Citation information

© Jan 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.