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Intermediate Algebra

Practice Test

Intermediate AlgebraPractice Test

Practice Test

447.

For the functions, f(x)=6x+1f(x)=6x+1 and g(x)=8x−3,g(x)=8x−3, find ⓐ (f∘g)(x),(f∘g)(x), ⓑ (g∘f)(x),(g∘f)(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.

ⓐ


ⓑ

450.

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

451.

Find the inverse of the function f(x)=x5−9.f(x)=x5−9.

452.

Graph the function g(x)=2x−3.g(x)=2x−3.

453.

Solve the equation 22x−4=64.22x−4=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(x2−39)=1log(x2−39)=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(x−3)=log724log7(x+2)+log7(x−3)=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?

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