Chapter 5 Review (College Algebra)

Chapter 5 Review

College Algebra

​Sections in Chapter 5

• 5.1 Inverse Functions

• 5.2 Exponential Functions

• 5.3 The Natural Exponential (e)

• 5.4 Intro to Logarithms

• 5.5 Properties of Logarithms

• 5.6 Exponential and Logarithmic Equations

Multiple Choice

How would this relation be classified?

• Function and one-to-one (injective)

• Function, but not one-to-one (injective)

• Not a function at all

Multiple Choice

Which functions are one-to-one?

A. $$f\left(x\right)=-2x^2-x+1$$

B. $$f\left(x\right)=-\frac{1}{3}x+7$$

C. $$f\left(x\right)=\sqrt[3]{x-1}+2$$

• A. only

• B. Only

• C. Only

• A. and B.

• B. and C.

Multiple Choice

Find the inverse of $$f\left(x\right)=9x-1$$ .

• $$f^{-1}\left(x\right)=x-\frac{1}{9}$$

• $$f^{-1}\left(x\right)=-9x+1$$

• $$f^{-1}\left(x\right)=\frac{x+1}{9}$$

• $$f^{-1}\left(x\right)=\frac{x-1}{9}$$

Multiple Select

If functions are truly inverses...

(select all that apply)

• their coordinates are switched (y,x).

• their graphs are reflected over the line y=x.

• they both pass through the origin (0,0).

• they intersect at only one (x,y) location.

Fill in the Blanks

Solve for x.

$25^{\ x-4}=125^{\ 4-x}$

x =

?

Multiple Choice

Which equation most accurately depicts the shown graph?

• $$y=2\cdot\left(\frac{1}{3}\right)^x$$

• $$y=2\cdot\left(3\right)^x$$

• $$y=3\left(\frac{1}{3}\right)^x-1$$

• $$y=2\cdot\left(\frac{1}{4}\right)^x$$

Fill in the Blanks

$50 is invested at 7% interest per year for 35 years, compounded semi-annually. What will be the collected amount at the end of the term? Round to the nearest cent.

Fill in the Blanks

What amount of principal would be required to reach $1300 if it is compounded continuously at 3.5% per year for 9 years? Round to the nearest cent.

Multiple Select

Select ALL expressions that are equivalent to each other.

• $$\log_28$$

• $$3\log_77$$

• $$\log_412$$

• $$\frac{1}{2}\log_{12}\left(12^6\right)$$

• $$\log_39$$

Multiple Choice

What is the domain of $$y=\log_7\left(x+1\right)$$ ?

• $$\left(0,\ \infty\right)$$

• $$\left(-1,\ \infty\right)$$

• $$\left(-\infty,\infty\right)$$

• $$\left(7,\ \infty\right)$$

• $$\left(1,\infty\right)$$

Multiple Choice

Solve for x.

$$\log_3\left(-x+1\right)=\log_3\left(2x+7\right)$$

• x = 2

• x = -2

• x = 1/2

• x = -7/2

• No Solution

Fill in the Blanks

Round $\log_47$ to 4 decimal places.

Multiple Choice

What is $$\left(\frac{1}{2}\right)^x=4f$$ in its logarithmic form?

• $$\log_{4f}\ x=\frac{1}{2}$$

• $$\log_x4f=\frac{1}{2}$$

• $$\log_{\frac{1}{2}}x=4f$$

• $$\log_{\frac{1}{2}}4f=x$$

Multiple Choice

Write $$3\log x^4-\log\left(\frac{1}{y^2}\right)+4\log\left(\frac{y}{x^3}\right)$$ as a single logarithm.

• $$6\log xy$$

• $$6\log y$$

• $$8\log x$$

• $$\frac{3}{4}\log xy$$

Fill in the Blanks

Solve for x. Round to the nearest hundredth (2 places.)

$2^{\left(2x-3\right)}=5^{\left(x-2\right)}$

That's it!

• Use this as a study guide to prep for your test!

• If some area(s) didn't go well, do something about it!

• The difficulty of these items is relatively close to the test items.