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Calculus I Problem Solving Session: Combining Functions, Shifting and Scaling Graphs, Study notes of Introduction to Philosophy

Lebanese American University Introduction to Philosophy

A problem solving session for calculus i students focusing on combining functions, shifting and scaling graphs. It includes various exercises and examples to help students understand the concepts of function composition, domain finding, and graph transformations. Students will learn how to find the domain of a sum or difference of functions, compose functions, and determine how the graph of one function can be obtained from another by shifting, scaling, and reflecting.

Typology: Study notes

2017/2018

Uploaded on 10/09/2018

leennnyoussef 🇱🇧

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MTH 101 – Calculus I

Problem Solving Session

1.2 – Combining Functions; Shifting and Scaling Graphs

Page 1 of 2

Combining Functions

1. Given 𝑓(𝑥)=√2𝑥 − 1 and 𝑔(𝑥)=𝑥 – 6

𝑥2−5𝑥+4

Find the domain of 𝑓 + 𝑔 and 𝑓

𝑔

2. Consider the functions 𝑓(𝑥)=√3 − 𝑥 and 𝑔(𝑥)=3𝑥−2

𝑥2−25

a) Find the domain of 𝑓.𝑔 and 𝑓

𝑔

b) Find 𝑔°𝑓(−6)

Composition of Functions

1. Consider the functions

𝑓(𝑥)=√3𝑥 + 2 , 𝑔(𝑥)= 𝑥2− 4𝑥 + 5 , and ℎ(𝑥)=3

𝑥

Find

a) 𝑓°𝑔(0)

b) 𝑓°𝑔(𝑥)

c) 𝑔°𝑓(𝑥)

d) ℎ°ℎ(𝑥)

2. Consider the functions

𝑓(𝑥)= 2𝑥 − 3 , 𝑔(𝑥)= 4 + √𝑥 , and ℎ(𝑥)= 𝑥2+ 1

Find

a) 𝑓°𝑔°ℎ(√8)

b) 𝑓°𝑔°ℎ(𝑥)

Discover Study notes of Introduction to Philosophy Lebanese American University

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MTH 101 – Calculus I

Problem Solving Session

1.2 – Combining Functions; Shifting and Scaling Graphs

Page 1 of 2

Combining Functions

Given 𝑓(𝑥) = √2𝑥 − 1 and 𝑔(𝑥) = (^) 𝑥 2 𝑥 – 6−5𝑥+ Find the domain of 𝑓 + 𝑔 and 𝑓𝑔
Consider the functions 𝑓(𝑥) = √3 − 𝑥 and 𝑔(𝑥) = (^) 𝑥3𝑥−2 (^2) − a) Find the domain of 𝑓. 𝑔 and 𝑓 𝑔 b) Find 𝑔°𝑓(−6)

Composition of Functions

Consider the functions 𝑓(𝑥) = √3𝑥 + 2 , 𝑔(𝑥) = 𝑥^2 − 4𝑥 + 5 , and ℎ(𝑥) = (^3) 𝑥

Find a) 𝑓°𝑔(0) b) 𝑓°𝑔(𝑥) c) 𝑔°𝑓(𝑥) d) ℎ°ℎ(𝑥)

Consider the functions 𝑓(𝑥) = 2𝑥 − 3 , 𝑔(𝑥) = 4 + √𝑥 , and ℎ(𝑥) = 𝑥^2 + 1

Find a) 𝑓°𝑔°ℎ(√8) b) 𝑓°𝑔°ℎ(𝑥)

MTH 101 – Calculus I

Problem Solving Session

1.2 – Combining Functions; Shifting and Scaling Graphs

Page 2 of 2

Shifting, Scaling, and Reflecting Graphs

Determine how the graph of 𝑔(𝑥) = 1 − 2√−𝑥 can be obtained from the graph of 𝑓(𝑥) = √𝑥 Explain your answer and sketch all steps.
Determine how the graph of 𝑔(𝑥) = |− 13 𝑥 + 1| − 2 can be obtained from the graph of 𝑓(𝑥) = |𝑥| Explain your answer and sketch all steps.
Given the graph of 𝑓(𝑥) a) Write down an expression for the graph of 𝑓(𝑥) reflected with respect to x- axis then vertically compressed by a factor 3 then shifted 2 units up. b) Sketch all steps. c) What is the range of the resulting function?

-6 -4 -2 2 4 6

Calculus I Problem Solving Session: Combining Functions, Shifting and Scaling Graphs, Study notes of Introduction to Philosophy

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Download Calculus I Problem Solving Session: Combining Functions, Shifting and Scaling Graphs and more Study notes Introduction to Philosophy in PDF only on Docsity!