Lynn Marecek; Andrea Honeycutt Mathis

Practice Test

For the functions, $f (x) = 6 x + 1$ and $g (x) = 8 x - 3,$ find ⓐ $(f \circ g) (x),$ ⓑ $(g \circ f) (x),$ and ⓒ $(f \cdot g) (x) .$

448.

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

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 $f (x) = x^{5} - 9 .$

452.

Graph the function $g (x) = 2^{x - 3} .$

453.

Solve the equation $2^{2 x - 4} = 64 .$

454.

Solve the equation $\frac{e^{x^{2}}}{e^{4}} = e^{3 x} .$

455.

Megan invested $$ 21,000$ in a savings account. If the interest rate is $5 %,$ 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: $10^{−2} = \frac{1}{100} .$

457.

Convert the equation from logarithmic equation to exponential form: $3 = {log}_{7} 343$

458.

Solve for x: ${log}_{5} x = −3$

459.

Evaluate ${log}_{11} 1 .$

460.

Evaluate ${log}_{4} \frac{1}{64} .$

461.

Graph the function
$y = {log}_{3} x .$

462.

Solve for x:
$log (x^{2} - 39) = 1$

463.

What is the decibel level of a small fan with intensity $10^{−8}$ watts per square inch?

464.

Evaluate each. ⓐ $6^{{log}_{6} 17}$
ⓑ ${log}_{9} 9^{−3}$

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

465.

${log}_{5} 25 a b$

466.

$ln \frac{e^{12}}{8}$

467.

${log}_{2} \sqrt[4]{\frac{5 x^{3}}{16 y^{2} z^{7}}}$

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

468.

$5 {log}_{4} x + 3 {log}_{4} y$

469.

$\frac{1}{6} log x - 3 log (x + 5)$

470.

Rounding to three decimal places, approximate ${log}_{4} 73 .$

471.

Solve for x:
${log}_{7} (x + 2) + {log}_{7} (x - 3) = {log}_{7} 24$

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

472.

${(\frac{1}{5})}^{x} = 9$

473.

$5 e^{x - 4} = 40$

474.

Jacob invests $14,000 in an account that compounds interest quarterly and earns $4 % .$ 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 $(A = 2 A_{0}) .$ How long will it take for that beetle population to triple?