Precalculus Class #: ______________ Section #: Instructor: Patricia Manderville Assignment: 1-5 Module One Problem Set Assignment Instructions: Do you need help with this problem or this material?

Remember to use the Academic Support resources available on your homepage in Brightspace or or in the learning modules. Question 1: (2 points) Solve the compound inequality: . Enter the exact answer in interval notation.

To enter , type infinity . , type U. Question 2: (4 points) Solve the inequality involving absolute value.

Enter the exact answer in interval notation.

To enter , type infinity . To enter , type U. Show your work and explain, in your own words, how you arrived at your answers. There are sample student explanations in the feedback to questions 3, 5, 9, and 14 that show the level of detail that is expected in your explanations.

4 ≤ 2 x − 8 < 10 ∞ ∪ |x − 3|+ 4 ≥ 13 ∞ ∪ 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 2/11 Question 3: (2 points) Solve the inequality involving absolute value.

Enter the exact answer in interval notation.

T o enter , type infinity . To enter , type U. Note: There is a sample student explanation given in the feedback to this question.

Question 4: (2 points) Describe all the -values at a distance of . Enter your answer in interval notation.

To enter , type infinity . To enter , type U. < 2 ? ? x− 4 5 ? ? ∞ ∪ x 21 11 ∞ ∪ 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 3/11 Question 5: (2 points) Find the domain of the rational function.

Enter your answer in interval notation.

T o enter , type infinity . To enter , type U. Note: There is a sample student explanation given in the feedback to this question.

Question 6: (4 points) Find the domain, vertical asymptotes, and horizontal asymptotes of the function.

Enter the domain in interval notation.

To enter , type infinity . To enter , type U. Domain: The fields below accept a list of numbers or formulas separated by semicolons (e.g. or ). The order of the lists do not matter .

Vertical asymptotes: Horizontal asymptotes: f (x)= x− 4 x+ 3 ∞ ∪ f (x)= x+ 4 − 16 x2 ∞ ∪ 2; 4; 6 x + 1; x − 1 x = y = 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 4/11 Question 7: (4 points) Find the - and -intercepts for the function. Enter your answers as points, . The -intercept is . The -intercept is . Show your work and explain, in your own words, how you arrived at your answers. There are sample student explanations in the feedback to questions 3, 5, 9, and 14 that show the level of detail that is expected in your explanations.

Question 8: (4 points) Find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the function. Use that information to sketch a graph.

Enter the intercepts as points, . The -intercept is . The -intercept is . The field below accepts a list of numbers or formulas separated by semicolons (e.g. or ). The order of the list does not matter .

Vertical asymptotes: Horizontal or slant asymptote: Select the correct sketch of the function. x y f (x)= x+ 10 + 16 x2 (a,b) x y f (x)= − x− 30 x2 − 25 x2 (a,b) x y 2; 4; 6 x + 1; x − 1 x = y = 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 5/11 (a) (b) 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 6/11 (c) (d) 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 7/11 (e) Question 9: (4 points) W rite an equation for a rational function with the given characteristics. Vertical asymptotes at and , -intercepts at and , horizontal asymptote at Enclose numerators and denominators in parentheses. For example, Include a multiplication sign between symbols. For example, . Note: There is a sample student explanation to this question given in the feedback to this question. x = − 1 x = 4 x (− 3,0) (1,0) y = − 3 (a − b)/(1 + n). a * x f (x)= 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 8/11 Question 10: (2 points) Simplify the expression.

Enter the exact answer .

Hint: You can write roots as fractional exponents, for example without needing a root symbol.

Question 1 1: (2 points) Simplify the expression.

Enter the exact answer .

Hints: You can write exponents with the ^ symbol, for example You can write square roots as sqrt, for example writing − 8 2 7 − −− √3 − 8 27 − −− √3 + 108 x6 − − −−− √ 27 x6 − − −− √ x6 108 x 6 − − −−−− √ 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 9/11 Question 12: (4 points) Use function composition to determine if (a) Y es, they are inverse functions. (b) No, they are not inverse functions. Show your work and explain, in your own words, how you arrived at your answers. There are sample student explanations in the feedback to questions 3, 5, 9, and 14 that show the level of detail that is expected in your explanations.

Question 13: (2 points) The circumference . a. Express the radius of a circle as a function of its circumference. Call this function . Enter the exact answer .

Enclose numerators and denominators in parentheses. For example, b. Find (a) The radius of a circle with a circumference of . (b) The radius of a circle with a circumference of . f (x) g(x) f (x)= x + 1 − − −− √3 g(x)= + 1 x3 C C (r)= 2πr r(C ) (a − b)/(1 + n). r(C )= r(20 π) r(20 π)= r(20 π) 20 π 20 π r(20 π) 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 10/11 Question 14: (2 points) Find the inverse of the function on the given domain. , Note: There is a sample student explanation given in the feedback to this question.

Question 15: (2 points) Find the inverse of the function.

Hint: The cube root is the same as an exponent of 1/3, so for , you could type in (19x)^(1/3). Remember your parentheses! Question 16: (2 points) Find the inverse of the function.

Enclose numerators and denominators in parentheses. For example, f (x)= (x − 1 3 )2 [13 ,∞ ) (x)= f− 1 f (x)= 9 − 3x3 19 x − − −− √3 (x)= f− 1 f (x)= x+ 2 x+ 4 (a − b)/(1 + n). (x)= f− 1 7/4/2021 Southern New Hampshire University - https://snhu.mobius.cloud/modules/unproctoredTest.Print 11/11 Question 17: (2 points) Find the inverse of the function. , Question 18: (4 points) The volume, , of a sphere in terms of its radius, , is given by . Express as a function of , and find the radius of a sphere with volume of cubic feet. Round your answer for the radius to two decimal places.

Enclose numerators and denominators in parentheses. For example, Include a multiplication sign between symbols. For example, . A sphere with volume cubic feet has radius feet. f (x)= 8 + 3x − 3 − − −−− √ (x)= f− 1 x ≥ 8 V r V (r)= 4 3 π r 3 r V 50 (a − b)/(1 + n). a π r(V )= 50

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