mymathlab section 2 1 homework answers

2.1 Linear Functions

m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 ; decreasing because m < 0. m < 0.

m = 1 , 868 − 1 , 442 2 , 012 − 2 , 009 = 426 3 = 142  people per year m = 1 , 868 − 1 , 442 2 , 012 − 2 , 009 = 426 3 = 142  people per year

y − 2 = − 2 ( x + 2 ) y − 2 = − 2 ( x + 2 ) ; y = − 2 x − 2 y = − 2 x − 2

y − 0 = − 3 ( x − 0 ) y − 0 = − 3 ( x − 0 ) ; y = − 3 x y = − 3 x

y = − 7 x + 3 y = − 7 x + 3

H ( x ) = 0.5 x + 12.5 H ( x ) = 0.5 x + 12.5

2.2 Graphs of Linear Functions

Possible answers include ( − 3 , 7 ) , ( − 3 , 7 ) , ( − 6 , 9 ) , ( − 6 , 9 ) , or ( − 9 , 11 ) . ( − 9 , 11 ) .

( 16 ,  0 ) ( 16 ,  0 )

• ⓐ f ( x ) = 2 x f ( x ) = 2 x
• ⓑ g ( x ) = − 1 2 x g ( x ) = − 1 2 x

y = – 1 3 x + 6 y = – 1 3 x + 6

• ⓐ ( 0 , 5 ) ( 0 , 5 )
• ⓑ ( 5 ,  0 ) ( 5 ,  0 )
• ⓓ Neither parallel nor perpendicular
• ⓔ Decreasing function
• ⓕ Given the identity function, perform a vertical flip (over the t -axis) and shift up 5 units.

2.3 Modeling with Linear Functions

• ⓐ C ( x ) = 0.25 x + 25 , 000 C ( x ) = 0.25 x + 25 , 000
• ⓑ The y -intercept is ( 0 , 25 , 000 ) . ( 0 , 25 , 000 ) . If the company does not produce a single doughnut, they still incur a cost of $25,000.

21.57 miles

2.4 Fitting Linear Models to Data

54 ° F 54 ° F

150.871 billion gallons; extrapolation

2.1 Section Exercises

Terry starts at an elevation of 3000 feet and descends 70 feet per second.

3 miles per hour

d ( t ) = 100 − 10 t d ( t ) = 100 − 10 t

Increasing.

Decreasing.

– 1 3 – 1 3

f ( x ) = − 1 2 x + 7 2 f ( x ) = − 1 2 x + 7 2

y = 2 x + 3 y = 2 x + 3

y = − 1 3 x + 22 3 y = − 1 3 x + 22 3

y = 4 5 x + 4 y = 4 5 x + 4

− 5 4 − 5 4

y = 2 3 x + 1 y = 2 3 x + 1

y = − 2 x + 3 y = − 2 x + 3

y = 3 y = 3

Linear, g ( x ) = − 3 x + 5 g ( x ) = − 3 x + 5

Linear, f ( x ) = 5 x − 5 f ( x ) = 5 x − 5

Linear, g ( x ) = − 25 2 x + 6 g ( x ) = − 25 2 x + 6

Linear, f ( x ) = 10 x − 24 f ( x ) = 10 x − 24

f ( x ) = − 58 x + 17.3 f ( x ) = − 58 x + 17.3

a. a = 11 , 900 a = 11 , 900 ; b = 1000.1 b = 1000.1 b. q ( p ) = 1000 p − 100 q ( p ) = 1000 p − 100

x = − 16 3 x = − 16 3

x = a x = a

y = d c − a x − a d c − a y = d c − a x − a d c − a

$45 per training session.

The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.

The slope is − 400. − 400. This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.

2.2 Section Exercises

The slopes are equal; y -intercepts are not equal.

The point of intersection is ( a , a ) . ( a , a ) . This is because for the horizontal line, all of the y y coordinates are a a and for the vertical line, all of the x x coordinates are a . a . The point of intersection will have these two characteristics.

First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation y = m x + b y = m x + b and solve for b . b . Then write the equation of the line in the form y = m x + b y = m x + b by substituting in m m and b . b .

neither parallel or perpendicular

perpendicular

( – 2 ,  0 ) ( – 2 ,  0 ) ; ( 0 , 4 ) ( 0 , 4 )

( 1 5 ,  0 ) ( 1 5 ,  0 ) ; ( 0 , 1 ) ( 0 , 1 )

( 8 ,  0 ) ( 8 ,  0 ) ; ( 0 ,  28 ) ( 0 ,  28 )

Line 1 : m = 8 Line 1 : m = 8 Line 2 : m = – 6 Line 2 : m = – 6 Neither Neither

Line 1 : m = – 1 2 Line 1 : m = – 1 2 Line 2 : m = 2 Line 2 : m = 2 Perpendicular Perpendicular

Line 1 : m = – 2 Line 1 : m = – 2 Line 2 : m = – 2 Line 2 : m = – 2 Parallel Parallel

g ( x ) = 3 x − 3 g ( x ) = 3 x − 3

p ( t ) = − 1 3 t + 2 p ( t ) = − 1 3 t + 2

( − 2 , 1 ) ( − 2 , 1 )

( − 17 5 , 5 3 ) ( − 17 5 , 5 3 )

• ⓐ g ( x ) = 0.75 x − 5.5 g ( x ) = 0.75 x − 5.5
• ⓒ ( 0 , − 5.5 ) ( 0 , − 5.5 )

x = − 3 x = − 3

no point of intersection

( 2 ,  7 ) ( 2 ,  7 )

( – 10 ,  –5 ) ( – 10 ,  –5 )

y = 100 x − 98 y = 100 x − 98

x < 1999 201 x > 1999 201 x < 1999 201 x > 1999 201

Less than 3000 texts

2.3 Section Exercises

Determine the independent variable. This is the variable upon which the output depends.

To determine the initial value, find the output when the input is equal to zero.

6 square units

20.012 square units

P ( t ) = 75 , 000 + 2,500 t P ( t ) = 75 , 000 + 2,500 t

(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.

Ten years after the model began.

W ( t ) = 0. 5 t + 7 . 5 W ( t ) = 0. 5 t + 7 . 5

( − 15 , 0 ) ( − 15 , 0 ) : The x -intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. ( 0 ,  7 . 5 ) ( 0 ,  7 . 5 ) : The baby weighed 7.5 pounds at birth.

At age 5.8 months.

C ( t ) = 12 , 025 − 205 t C ( t ) = 12 , 025 − 205 t

(58.7, 0) (58.7, 0) : In roughly 59 years, the number of people inflicted with the common cold would be 0. (0,12,025) (0,12,025) : Initially there were 12,025 people afflicted by the common cold.

y = − 2 t +180 y = − 2 t +180

In 2070, the company’s profit will be zero.

y = 30 t − 300 y = 30 t − 300

(10, 0) In 1990, the profit earned zero profit.

During the year 1933

• ⓐ 696 people
• ⓒ 174 people per year
• ⓓ 305 people
• ⓔ P ( t ) = 305 + 174 t P ( t ) = 305 + 174 t
• ⓕ 2,219 people
• ⓐ C ( x ) = 0.15 x + 10 C ( x ) = 0.15 x + 10
• ⓑ The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
• ⓐ P ( t ) = 190 t + 4360 P ( t ) = 190 t + 4360
• ⓑ 6,640 moose
• ⓐ R ( t ) = 16 − 2.1 t R ( t ) = 16 − 2.1 t
• ⓑ 5.5 billion cubic feet
• ⓒ During the year 2017

More than 133 minutes

More than $42,857.14 worth of jewelry

2.4 Section Exercises

When our model no longer applies, after some value in the domain, the model itself doesn’t hold.

We predict a value outside the domain and range of the data.

The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.

61.966 years

Interpolation. About 60 °  F . 60 °  F .

Yes, trend appears linear because r = 0. 985 r = 0. 985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.

y = 1 . 64 0 x + 13 . 8 00 y = 1 . 64 0 x + 13 . 8 00 , r = 0. 987 r = 0. 987

y = − 0.962 x + 26.86 , r = − 0.965 y = − 0.962 x + 26.86 , r = − 0.965

y = − 1 . 981 x + 6 0. 197 y = − 1 . 981 x + 6 0. 197 ; r = − 0. 998 r = − 0. 998

y = 0. 121 x − 38.841 , r = 0.998 y = 0. 121 x − 38.841 , r = 0.998

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −2 0 ) , ( 6 , −22 ) , ( 9 , −28 ) ( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −2 0 ) , ( 6 , −22 ) , ( 9 , −28 ) ; y = −2 x −10 y = −2 x −10

( 189 . 8 , 0 ) ( 189 . 8 , 0 ) If 18,980 units are sold, the company will have a profit of zero dollars.

y = 0.00587 x + 1985 .4 1 y = 0.00587 x + 1985 .4 1

y = 2 0. 25 x − 671 . 5 y = 2 0. 25 x − 671 . 5

y = − 1 0. 75 x + 742 . 5 0 y = − 1 0. 75 x + 742 . 5 0

Review Exercises

y = − 3 x + 26 y = − 3 x + 26

y = 2 x − 2 y = 2 x − 2

Not linear.

( –9 , 0 ) ; ( 0 , –7 ) ( –9 , 0 ) ; ( 0 , –7 )

Line 1: m = − 2 ; m = − 2 ; Line 2: m = − 2 ; m = − 2 ; Parallel

y = − 0.2 x + 21 y = − 0.2 x + 21

y = − 3 00 x + 11 , 5 00 y = − 3 00 x + 11 , 5 00

a) 800 ; b) 100 students per year ; c) P ( t ) = 100 t + 1700 P ( t ) = 100 t + 1700

Extrapolation.

Midway through 2024.

y = − 1.294 x + 49.412 ; r = − 0.974 y = − 1.294 x + 49.412 ; r = − 0.974

Early in 2022

Practice Test

y = −1.5 x − 6 y = −1.5 x − 6

y = − 2 x − 1 y = − 2 x − 1

Perpendicular

( − 7 , 0 ) ( − 7 , 0 ) ; ( 0 , − 2 ) ( 0 , − 2 )

y = − 0.25 x + 12 y = − 0.25 x + 12

y = 875 x + 10 , 675 y = 875 x + 10 , 675

a) 375 ; b) dropped an average of 46.875, or about 47 people per year ; c) y = − 46.875 t + 1250 y = − 46.875 t + 1250

Early in 2018

y = 0.00455 x + 1979.5 y = 0.00455 x + 1979.5

r = 0.999 r = 0.999

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Access for free at https://openstax.org/books/precalculus/pages/1-introduction-to-functions

• Authors: Jay Abramson
• Publisher/website: OpenStax
• Book title: Precalculus
• Publication date: Oct 23, 2014
• Location: Houston, Texas
• Book URL: https://openstax.org/books/precalculus/pages/1-introduction-to-functions
• Section URL: https://openstax.org/books/precalculus/pages/chapter-2

© Dec 8, 2021 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

• For educators

Intermediate Algebra plus MyMathLab/MyStatLab -- Access Card Package (11th Edition) Edit edition This problem has been solved: Solutions for Chapter 2.1 …

Hence the given form is a linear equation.

It is a polynomial of degree 2.

Corresponding textbook

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