## Linear Functions 32 Exercises

**Vocabulary and Core Concept Check**

Question 1.**COMPLETE THE SENTENCE**A 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 MATHEMATICS**The 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 STRUCTURE**How 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.**REASONING**The 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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## Lesson 34 Graphing Linear Equations In Standard Form

**Essential Question**How 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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