MAC 1105Test 3 Review andPractice Solutions

MAC 1105 Test 3 Review 2.4 – 2.9, 3.1, 3.6, 3.8• You will need to have your own graphing calculator for the test. • You may not share calculators or use any type of communication device in place of a calculator. • Tests cannot be made up for any reason other than an NWFSC event for which you must miss class. • If you miss one test, your final exam score will be substituted. A second missed test is a zero.

Exam TopicsObjective Section Suggested Text Problems1) Determine the domain and relation of a relation and indicated whether or not it is a function. 2.4 Page 294: 49

2) Find function values. 2.4 p. 224: 29, 313) Find the domain of a function. 2.4 p. 225: 41, 434) Use your calculator to find intervals of increasing and decreasing. 2.5 p. 236: 135) Classify a function as even, odd, or neither. 2.5 p. 294: 87, 89(even, odd, neither)6) Evaluate a difference quotient. 2.5 p. 239: 797) Write a linear function given two function values. 2.6 p. 248: 9, 11, 138) Find function values of a piece-wise function. 2.6 p. 248: 19(values)9) Graph a piece-wise function. 2.6 p. 248: 19(graph)10) Indicate the transformations that have occurred to produce the given function. 2.7 (see notes)11) Write the equation of a function whose graph has been transformed. 2.7 p. 265: 67, 69, 71, 7312) Perform operations on functions. 2.8 p. 294: 63, 6513) Find the composition of two functions 2.8 p. 294: 69, 7114) Find the inverse of a linear function. 2.9 p. 288: 41 15) Find the inverse of a rational function. 2.9 p. 294: 10116) Find the vertex of a quadratic function 3.1 P. 397:7 17) Work a max/min quadratic application. 3.1 p. 399: 10118) Find the domain of a rational function. 3.6 p. 372: 7, 9, 11, 1319) Find any vertical or horizontal asymptotes for a given rational function. 3.6 p. 373: 29, 21, 3720) Work a variation application. 3.8 p. 399: 111

To Study for the Test• Complete all assigned homework. Remember that a score of at least 70% on each assignment gives you 10 bonus points on the test.• Complete the practice test and check your solutions.• Set up a study system (note cards for example) for each of the 20 objectives in the chart above.• Review your notes and applicable problem set questions for each of the 20 objectives in the chart above.• Work the suggested text problems for each of the 20 objectives in the chart above.

1) Give the domain and range of each relation. Indicate whether the relation is a function by writing “yes” or “no”.

a) Domain: {1, 2, 3, 4, 5}Range: The relation is not a function since 1 is associated with both 3 and  b) Domain: Range: The relation is a function.

2) Let Find the following function values.

 

 

 

3) Find the domain of each function (in interval notation). a)

  

4) Graph the following function in your graphing calculator and determine the intervals where the function is increasing and the intervals where the function is decreasing.

Increasing: Decreasing:

5) Classify the function as even, odd, or neither..

6) Evaluate the difference quotient for the function

7) Find a linear function such that and

8) Find for the following piece–wise function.

Graph the function in problem 8. 𝑓 (𝑥 )={3+𝑥𝑖𝑓 ∧−3<𝑥≤01−𝑥𝑖𝑓 ∧0<𝑥<5

10) Circle the correct answer in each case to indicate what happens to the graph at each step.This is how the right-hand side changes How is the graph transformed?

The graph is shifted 4 units to the right.The graph is shifted 4 units to the left. The graph is shifted 4 units downward. The graph is shifted 4 units upward.The graph is stretched vertically by a factor of 2.The graph is stretched horizontally by a factor of 2.The graph is shrunk vertically by a factor of .The graph is shrunk horizontally by a factor of  The graph is reflected about the x-axis.The graph is reflected about the y-axis.The graph is shifted 3 units to the right.The graph is shifted 3 units to the left. The graph is shifted 3 units downward. The graph is shifted 3 units upward.

11) Write an equation for the function whose graph fits the following description.The graph of is shifted four units right, reflected in the y-axis and shifted two units up

  

12) Let and a) Find

12b) Find Simplify your answer completely.

12c) Find 12d) Find

13) Let . Find . Simplify your answer completely.

14) Find the inverse of the following function.

15) Find the inverse of the following function.

16) Find the vertex of the quadratic function .

 

17) The function can be used to model the height of a pumpkin launched by an air cannon after the pumpkin has traveled feet.What is the maximum height of the pumpkin (rounded to the nearest foot)? 

 

 18) Find the domain of .

19) Let a) Find the vertical asymptote(s) of the function.

Write (not  b) Find the horizontal asymptote(s) of the function.Write (Not 2)

20) The stress in the material of a pipe varies jointly with the internal pressure and internal diameter of the pipe and inversely with the thickness of the pipe. The stress is 100 pounds per square inch when the diameter is 5 inches, the thickness if 0.75 inches, and the internal pressure is 25 pounds per square inch. Find the stress when the internal pressure is 50 pounds per square inch, the diameter is six inches, and the thickness is 0.5 inch.

 

Test 3 Extra Practice

1) Give the domain and range of the relation. Indicate whether the relation is a function.

1) Give the domain and range of the relation. Indicate whether the relation is a function. Domain: {0, 1, 2, 3} Range: {} The relation is a function. 

a) b) c) 2) Let Find the following function values. Simplify completely.

2) Let Find the following function values. Simplify completely.a) b) c) a) , b) c)

3) Find the domain of each function. Write your answer in interval notation.a) b)

a) b) a) b)

3) Find the domain of each function. Write your answer in interval notation.

4) Graph the following function in your graphing calculator and determine the intervals where the function is increasing and the intervals where the function is decreasing. Be sure to enlarge the window enough to view both turning points. The turning points have integer coordinates.

4) Graph the following function in your graphing calculator and determine the intervals where the function is increasing and the intervals where the function is decreasing. Be sure to enlarge the window enough to view both turning points. The turning points have integer coordinates.

5) Classify the function as even, odd, or neither: .

5) Classify the function as even, odd, or neither: .

 

6) Evaluate the difference quotient for the function

6) Evaluate the difference quotient for the function

7) Find a linear function such that and

7) Find a linear function such that and two points:

8) Find the function values for the following piece-wise function.

8) Find the function values for the following piece-wise function.

9) Carefully graph the function in problem 8.

 

10) Indicate what happens to the graph at each step.

10) Indicate what happens to the graph at each step.

11) Write an equation for the function whose graph fits the following description.The graph of is shifted four units right, reflected in the y-axis and shifted five units up.

11) Write an equation for the function whose graph fits the following description.The graph of is shifted four units right, reflected in the y-axis and shifted five units up.

12) Let and

a) Find (7) b) Find Simplify your answer completely.

12) Let and

a) Find  b) Find Simplify your answer completely.

13) Let . Find . Simplify your answer completely.

13) Let . Find . Simplify your answer completely.

14) Find the inverse of the following function.

14) Find the inverse of the following function.

15) Find the inverse of the following function.

15) Find the inverse of the following function.

16) Find the vertex of the quadratic function . Write the vertex as a point (ordered pair).

16) Find the vertex of the quadratic function . Write the vertex as a point (ordered pair).

17) The height h (in feet) of a leaping lizard can be modeled by the quadratic function where is the horizontal distance from the lizard’s starting point.What is the maximum height the lizard achieves?

 

17) The height h (in feet) of a leaping lizard can be modeled by the quadratic function where is the horizontal distance from the lizard’s starting point.What is the maximum height the lizard achieves?

 

18) Find the domain of .

18) Find the domain of .

19) a) Find the vertical asymptote(s) of the function. b) Find the horizontal asymptote(s) of the function.

19) a) Find the vertical asymptote(s) of the function.

(cancel the only for VA’s)

b) Find the horizontal asymptote(s) of the function. degrees are equal

20) varies directly with and and inversely with the cube of If is 0.256 when and , find when and

20) varies directly with and and inversely with the cube of If is 0.256 when and , find when and