Linear Functions 32 Exercises
Vocabulary and Core Concept Check
Question 1.COMPLETE THE SENTENCEA linear equation in two variables is an equation that can be written in the form ________, where m and b are constants.Answer:
y = 4x 4x y = 32x 4x²Compare the above equation with the standard representation of the linear functionThe standard representation of the linear function is:y = mx + cWe can conclude that the given equation is not a linear function
Question 21.2 + \ y = 3x + 4Answer:
y x = 2x \yAnswer:The given equation is a linear fraction
Explanation:y x = 2x \ySo,y + \y = 2x + x\ + \ = 3x\y = 3xy = 3x × \y = \x + 0Compare the above equation with the standard representation of the linear functionThe standard representation of the linear function is:y = mx + cWe can conclude that the given equation is a linear function
Question 23.
The domain is the range of all the values of xNow,The domain of the given function is: 0, 1, 2, 3, 4, 5, and 6From the given graph,We can observe that the domain of the given graph is continuous because there are not any unconnected points in the graph
Question 35.MODELING WITH MATHEMATICSThe linear function m = 55 8.5b represents the amount m of money that you have after buying b books.a. Find the domain of the function. Is the domain discrete or continuous? Explain.b. Graph the function using its domain.Answer:
b.The representation of the function with the domain in the coordinate plane is:
Question 45.
Maintaining Mathematical Proficiency
Question 55.
Graphing Linear Functions Cumulative Assessment
Question 1.You claim you can create a table of values that represents a linear function. Your friend claims he can create a table of values that represents a nonlinear function. Using the given numbers, what values can you use for x and y to support your claim? What values can your friend use?Answer:It is given that you claim you can create a table of values that represents a linear function. Your friend claims he can create a table of values that represents a nonlinear function.Hence,The values you and your friend use are:
Question 2.A car rental company charges an initial fee of $42 and a daily fee of $12.a. Use the numbers and symbols to write a function that represents this situation.b. The bill is $138. How many days did you rent the car?Answer:a.It is given that a car rental company charges an initial fee of $42 and a daily fee of $12So,The function that represents the situation is:f = × xf = 52xx is the number of days that you rent the car
b.It is given that the bill is: $138So,
The given compound inequality is:2 | x 5 | < 162 < 16 an d 2 > -162x 10 < 16 and 2x 10 > -162x < 26 and 2x > -6x < 13 and x > -3Hence,The solution of the given compoud inequality is: -3 < x < 13Now,The sum of all the integers = -2 1 + 0 + 1 + 2 + 3 + 4 + 5+ 6 + 7 + 8 +9 + 10 + 11 + 12= 75We can conclude that the sum of all the integers is: 75
Graphing Absolute Value Functions 37 Exercises
Vocabulary and Core Concept Check
Question 1.The point is the _______ of the graph of f = -3 | x 1 | 4.Answer:
Question 2.USING STRUCTUREHow do you know whether the graph of f = a | x h | + k is a vertical stretch or a vertical shrink of the graph of f = | x | ?Answer:f = a | x h | + kWhere,a is the vertical stretch or vertical shrinkh is the horizontal translationk is the vertical shiftNow,a will be the vertical stretch if the value of a is an integera will be the vertical shrink if the value of a is a fractionHence, from the above,We can conclude that the given function is a vertical stretch
Question 3.Describe three different types of transformations of the graph of an absolute value function.Answer:
Question 4.REASONINGThe graph of which function has the same y-intercept as the graph of f = | x 2 | + 5? Explain.Answer:The given absolute value functions are:a. f = | x 2 | + 5b. g = | 3x 2 | + 5c. h = 3 | x 2 | + 5We know that,| x | = x for x > 0| x | = -x for x < 0Now,The given absolute value function is:f = | x 2 | + 5So,f = x 2 + 5 or f = – + 5f = x + 3 or f = -x + 2 + 5f = x + 3 or f = -x + 7
b.The given absolute value function is:g = | 3x 2 | + 5So,g = 3x 2 + 5 or g = + 5g = 3x + 3 or g = -3x + 2 + 5g = 3x + 3 or g = -3x + 7
a is the vertical stretchFrom the graph,We can observe that the vertical stretch occurs at Hence, from the above,We can conclude that the value of a is: 2
Question 23.vertical translation 7 units downAnswer:
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Solving Linear Inequalities Chapter Test
Write the sentence as an inequality.
Question 1.The sum of a number y and 9 is at least -1.Answer:The given worded form is:The sum of a number y and 9 is at least -1Hence,The representation of the given worded form in the form of inequality is:y + 9 -1
A number r is more than 0 or less than or equal to -8.Answer:The given worded form is:A number r is more than 0 or less than or equal to -8Hence,The representation of the given worded form in the form of inequality is:r > 0 or r -8
Question 3.A number k is less than 3 units from 10.Answer:The given worded form is:A number k is less than 3 units from 10Hence,The representation of the given worded form in the form of inequality is:k 10 < 3
Solve the inequality. Graph the solution, if possible.
Question 4.\ 5 -9Answer:\ 5 -9\ -9 + 5\ -4
We can conclude that the solution to the given inequality is -3 a 2The representation of the solution of the inequality in the graph is:
Question 9.-5 < 2 h or 6h + 5 > 71Answer:-5 < 2 h or 6h + 5 > 71-5 2 < h or 6h > 71 5-7 < -h or 6h > 667 < h or h > 66 / 6h > 7 or h > 11Hence, from the above,We can conclude that the solution to the given inequality is h > 7 The representation of the solution of the given inequality in the graph is:
Question 15.Let a, b, c, and d be constants. Describe the possible solution sets of the inequality ax + b < cx + d.Answer:
The values of a and b so that the inequality has no solution are:a = 3 and b < 4
Solving Linear Inequalities Chapter Review
2.1 Writing and Graphing Inequalities a. A number x plus 36 is no more than 40. Write this sentence as an inequality.b. Graph w > 3.
Write the sentence as an inequality.
Question 1.A number d minus 2 is less than -1.Answer:The given worded form is:A number d minus 2 is less than -1Hence,The representation of the given worded form in the form of inequality is:d 2 < -1
Ten is at least the product of a number h and 5.Answer:The given worded form is:Ten is at least the product of a number h and 5Hence,The representation of the given worded form in the form of inequality is:10 h
We can conclude that there is no solution to the given inequality
2.5 Solving Compound Inequalities
Solve 1 2d + 7 9. Graph the solution.
Question 21.A number x is more than -6 and at most 8. Write this sentence as an inequality. Graph the inequality.Answer:The given worded form is:A number x is more than -6 and at most 8The representation of the given worded form in the form of inequality is:x > -6 and x 8Hence,The representation of the solutions of the given worded form in the form of compound inequality is:-6 < x 8The representation of the compound inequality in the graph is:
Solve the inequality. Graph the solution.
Question 22.We can conclude that the compound inequality solution to the given inequality is:-2 z 6The representation of the compound inequality in the graph is:
2.6 Solving Absolute Value Inequalities
Solve the inequality. Graph the solution, if possible.
Question 24.
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Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions
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The Big Ideas Math Algebra 1 Answer Key Ch 3 Graphing Linear Functions includes Questions from Exercises 3.1 to 3.7, Chapter Tests, Practice Tests, Cumulative Assessment, Review Tests, etc. Practice using the BIM Algebra 1 Graphing Linear Functions Solution Key and learn all the fundamentals involved. Big Ideas Math Algebra 1 Ch 3 Graphing Linear Functions Answer Key is available free of cost and you can prepare using it anytime and anywhere.
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Lesson 34 Graphing Linear Equations In Standard Form
Essential QuestionHow can you describe the graph of the equation Ax + By = C?Answer:When A and B are not both zero,The graph of Ax + By = C is always a line.Now,Divide both sides by BBecause the form Ax + By = C can describe any line,It is called the standard form of an equation for a line.
EXPLORATION 1Using a Table to Plot PointsWork with a partner. You sold a total of $16 worth of tickets to a fundraiser. You lost track of how many of each type of ticket you sold. Adult tickets are $4 each. Child tickets are $2 each.a. Let x represent the number of adult tickets. Let y represent the number of child tickets. Use the verbal model to write an equation that relates to x and y.Answer:It is given that you sold a total of $16 worth of tickets to a fundraiser. You lost track of how many of each type of ticket you sold. Adult tickets are $4 each. Child tickets are $2 each.It is also given thatLet x be the number of adult ticketsLet y be the number of child ticketsSo,The total cost of tickets = The total cost of tickets = × + × So,We can conclude that the equation that relates x and y is:x + 2y = 8
b. Copy and complete the table to show the different combinations of tickets you might have sold.Answer:The equation that represents the number of different tickets sold is:x + 2y = 8y = \So,The completed table that shows the different combinations of tickets you might have sold is:
Communicate Your Answer
3.4 Lesson
The x-intercept is: The y-intercept is:
Question 29.
Question 6.
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Function Notation 33 Exercises
Vocabulary and Core Concept Check
Question 1.When you write the function y = 2x + 10 as f = 2x + 10, you are using ______________.Answer:
Question 2.REASONING Your height can be represented by a function h, where the input is your age. What does h represent?Answer:It is given that your height can be represented by a function h, where the input is your ageSo,h means you are 14 years old
Monitoring Progress and Modeling with Mathematics
In Exercises 310, evaluate the function when x = 2, 0, and 5.
Question 3.
We can conclude that the value of the given function is: 5
Question 17.q = \x 3 q = -4Answer:
j = \x + 7 j = -5Answer:j = \x + 7 with j = -5So,-5 = \x + 7-5 7 = \x\x = -12\x = 12x = 12 × \x = 15We can conclude that the value of the given function is: 15
In Exercises 19 and 20, find the value of x so that f = 7.
Question 19.
h = -5Now,put the values -2, -1, 0, 1, 2 in the place of x and find the values of f to plot a graph So,The completed table for the given function is:Hence,The representation of the given function in the coordinate plane is:
Question 25.d = \ 3Answer:
w = \ + 2Answer:w = \ + 2So,w = \ x + 2Now,put the values -2, -1, 0, 1, 2 in the place of x and find the values of f to plot a graph So,The completed table for the given function is:Hence,The representation of the given function in the coordinate plane is:
Question 27.
Mathematical Practices
Find the domain and range of the function represented by the graph.
Question 3.
Question 8.
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