Find the domain, x-intercept, and asymptote of the logarithmic function. f ( x ) = − log ⁡ 10 x − 6 f\left(x\right)=-\log_{10}x-6 f ( x ) = − lo g 1 0 x − 6

domain: ( 0 , ∞ ) \left(0,\infty\right) ( 0 , ∞ ) x-intercept: (0,0) asymptote: x = 0

domain: ( 0 , ∞ ) \left(0,\infty\right) ( 0 , ∞ ) x-intercept: (0,0) asymptote: y = 0

Find the domain, x-intercept, and asymptote of the logarithmic function. f ( x ) = ln ⁡ ( x + 4 ) f\left(x\right)=\ln\left(x+4\right) f ( x ) = ln ( x + 4 )

domain: ( − 4 , ∞ ) \left(-4,\infty\right) ( − 4 , ∞ ) x-intercept: (-3,0) asymptote: x = -4

domain: ( − 4 , ∞ ) \left(-4,\infty\right) ( − 4 , ∞ ) x-intercept: (0,-3) asymptote: x = -4

Use the properties of logarithms to condense the expression. log ⁡ 3 13 + log ⁡ 3 y \log_313+\log_3y lo g 3 1 3 + lo g 3 y

log ⁡ 3 13 y \log_313y lo g 3 1 3 y

13 log ⁡ 3 y 13\log_3y 1 3 lo g 3 y

y log ⁡ 3 13 y\log_313 y lo g 3 1 3

Precalculus Chapter 3 Test

Quiz

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.BF.B.5, HSF-IF.C.7E, HSA.SSE.B.3

+4

Standards-aligned

Montana Hise

Used 76+ times

FREE Resource

About this resource

This quiz covers exponential and logarithmic functions, which represents a fundamental chapter in Precalculus typically taught at the 11th and 12th grade levels. The questions systematically assess students' understanding of core concepts including exponential function properties and asymptotes, logarithmic simplification using inverse properties, domain and range determination for logarithmic functions, numerical evaluation of logarithms, expansion and condensation of logarithmic expressions using product and power rules, and solving exponential and logarithmic equations. Students need to demonstrate mastery of logarithm properties such as the inverse relationship between exponentials and logarithms (log_b(b^x) = x), the product rule (log(ab) = log(a) + log(b)), the power rule (log(a^n) = n·log(a)), and change of base formulas. They must also understand function transformations, identify vertical asymptotes and domains of logarithmic functions, and apply algebraic manipulation techniques to solve equations involving these functions. Created by Montana Hise, a Mathematics teacher in US who teaches grade 11 and 12. This assessment serves as a comprehensive chapter test that evaluates student mastery of exponential and logarithmic functions through varied problem types requiring both conceptual understanding and computational skills. Teachers can use this quiz as a summative assessment following instruction on Chapter 3 of their Precalculus curriculum, or break it into smaller sections for formative assessment during the unit. The mix of graph analysis, algebraic manipulation, and equation-solving problems makes it suitable for review sessions before major exams or as a homework assignment to reinforce learning. The quiz aligns with Common Core standards A-SSE.3c (using properties of exponents to transform expressions) and F-LE.4 (expressing exponential and logarithmic functions in equivalent forms), supporting students' preparation for advanced mathematics courses and standardized assessments.

15 questions

Show all answers

1.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Identify the correct graph of the following function and identify any asymptotes.
$f\left(x\right)=10^{-x}$

Horizontal asymptote: y = 0

horizontal asymptote: x = 0

Tags

CCSS.HSF-IF.C.7E

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Use the properties of logarithms to simply the expression.
$f\left(x\right)=\log_77^{-.089}$

-7

7

-.89

-.089

Tags

CCSS.HSF.BF.B.5

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Use the properties of logarithms to simplify the expression.
$f\left(x\right)=5-\log_{10}1000$

5

2

3.78

.2

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the domain, x-intercept, and asymptote of the logarithmic function.
$f\left(x\right)=-\log_{10}x-6$

domain: $\left(0,\infty\right)$

x-intercept: (0,0)

asymptote: y = 0

domain: $\left(-\infty,\infty\right)$

x-intercept: (0,0)

asymptote: x = 0

domain: $\left(0,\infty\right)$

x-intercept: (0,0)

asymptote: x = 0

Tags

CCSS.HSF-IF.C.7E

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the domain, x-intercept, and asymptote of the logarithmic function.
$f\left(x\right)=\ln\left(x+4\right)$

domain: $\left(-\infty,\infty\right)$

x-intercept: (-3,0)

asymptote: y = -4

domain: $\left(-4,\infty\right)$

x-intercept: (-3,0)

asymptote: x = -4

domain: $\left(-4,\infty\right)$

x-intercept: (0,-3)

asymptote: x = -4

Tags

CCSS.HSF-IF.C.7E

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate. $\log_744$

1.94

1.98

.194

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

7.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Evaluate. $\log_{\frac{2}{5}}1.3$

.29

-.29

-0.29

-.029

Tags

CCSS.HSF.BF.B.5

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

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Precalculus Chapter 3 Test

15 questions

Identify the correct graph of the following function and identify any asymptotes.
$f\left(x\right)=10^{-x}$

Use the properties of logarithms to simply the expression.
$f\left(x\right)=\log_77^{-.089}$

Use the properties of logarithms to simplify the expression.
$f\left(x\right)=5-\log_{10}1000$

Find the domain, x-intercept, and asymptote of the logarithmic function.
$f\left(x\right)=-\log_{10}x-6$

Find the domain, x-intercept, and asymptote of the logarithmic function.
$f\left(x\right)=\ln\left(x+4\right)$

Evaluate. $\log_744$

Evaluate. $\log_{\frac{2}{5}}1.3$

Evaluate. $\log_{12}64$

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple logarithms.
$\log_23a^4$

Use the properties of logarithms to condense the expression.
$\log_313+\log_3y$

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Precalculus Chapter 3 Test

15 questions

Identify the correct graph of the following function and identify any asymptotes. f(x)=10−xf\left(x\right)=10^{-x}f(x)=10−x

Use the properties of logarithms to simply the expression. f(x)=log⁡77−.089f\left(x\right)=\log_77^{-.089}f(x)=log7​7−.089

Use the properties of logarithms to simplify the expression. f(x)=5−log⁡101000f\left(x\right)=5-\log_{10}1000f(x)=5−log10​1000

Find the domain, x-intercept, and asymptote of the logarithmic function. f(x)=−log⁡10x−6f\left(x\right)=-\log_{10}x-6f(x)=−log10​x−6

Find the domain, x-intercept, and asymptote of the logarithmic function. f(x)=ln⁡(x+4)f\left(x\right)=\ln\left(x+4\right)f(x)=ln(x+4)

Evaluate. log⁡744\log_744log7​44

Evaluate. log⁡251.3\log_{\frac{2}{5}}1.3log52​​1.3

Evaluate. log⁡1264\log_{12}64log12​64

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple logarithms. log⁡23a4\log_23a^4log2​3a4

Use the properties of logarithms to condense the expression. log⁡313+log⁡3y\log_313+\log_3ylog3​13+log3​y

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Identify the correct graph of the following function and identify any asymptotes.
$f\left(x\right)=10^{-x}$

Use the properties of logarithms to simply the expression.
$f\left(x\right)=\log_77^{-.089}$

Use the properties of logarithms to simplify the expression.
$f\left(x\right)=5-\log_{10}1000$

Find the domain, x-intercept, and asymptote of the logarithmic function.
$f\left(x\right)=-\log_{10}x-6$

Find the domain, x-intercept, and asymptote of the logarithmic function.
$f\left(x\right)=\ln\left(x+4\right)$

Evaluate. $\log_744$

Evaluate. $\log_{\frac{2}{5}}1.3$

Evaluate. $\log_{12}64$

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple logarithms.
$\log_23a^4$

Use the properties of logarithms to condense the expression.
$\log_313+\log_3y$