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Decide which of the two given functions is linear, and find its equation. HINT [See Example 1.] -10 10 20 30 f(x) -5.5 5.5 6.5 7.5 g(x) -3 -1 3

Decide which of the two given functions is linear, and find its equation. HINT [See Example 1.] -10 10 20 30 f(x) -5.5 5.5 6.5 7.5 g(x) -3 -1 3

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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Recall that a linear function is one that can be written as h(x) = mx + b or y = mx + b, wherem and b are fixed numbers. Ду = m is the slope. Ax Recall also that if y = mx + b, then a change of Ax units in x results in a change of Ay = m(Ax) units in y, so that Af To determine whether f(x) (or g(x)) is a linear function, we must find out whether or not the ratio Ag or is always the same. Ax Ax First we consider f(x). -10 10 20 30 f(x) -5.5 5.5 6.5 7.5 Af when x changes from x, = -10 to x, = 0. Ax We start by using the table to find the ratio Af f(x2) - f(x1) Ax X2 - X1 f(0) – f 0 - (-10) 0 - (-10)
Transcribed Image Text:Recall that a linear function is one that can be written as h(x) = mx + b or y = mx + b, wherem and b are fixed numbers. Ду = m is the slope. Ax Recall also that if y = mx + b, then a change of Ax units in x results in a change of Ay = m(Ax) units in y, so that Af To determine whether f(x) (or g(x)) is a linear function, we must find out whether or not the ratio Ag or is always the same. Ax Ax First we consider f(x). -10 10 20 30 f(x) -5.5 5.5 6.5 7.5 Af when x changes from x, = -10 to x, = 0. Ax We start by using the table to find the ratio Af f(x2) - f(x1) Ax X2 - X1 f(0) – f 0 - (-10) 0 - (-10)
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Decide which of the two given functions is linear, and find its equation. HINT [See Example 1.] -10 10 20 30 f(x) -5.5 5.5 6.5 7.5 g(x) -3 -1 1
Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Decide which of the two given functions is linear, and find its equation. HINT [See Example 1.] -10 10 20 30 f(x) -5.5 5.5 6.5 7.5 g(x) -3 -1 1
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