# Basic Functions and Their Graphs - Arizona State University

Combining Functions Section 1.7 Objectives Determine the domain and range (where possible) of a function given as an equation. Add, subtract, multiply, and/or divide function. State the domain two function combined in an arithmetic method.

Put together two (or more) functions using composition. Determine the value of the composition of two (or more) functions given the graphs of the functions. Determine the value of the composition of two (or more) function given the equations of the functions. State the domain two function combined through composition.

Objectives Decompose the composition of two functions into it constituent functions. Solve a word problem involving the composition of functions. Vocabulary domain range

function composition Domain Questions 1. Does the function have a denominator? 2. Does the function have a square or even root? 3. Does the function have a log or ln in it?

4. Did the function arise from finding an inverse? 5. Is this a real world problem? Find the domain of the function: x 11 h(x ) 2 x 196

Find the domain of the function: f (x ) 67.5 5x Find the domain of the function: g(x ) 8x 2 4

Find the domain of the function: k (x ) 4 x 17 15 the functionsf (x ) x 5 8 Given

andg(x ) x 9 find each of the following: (f g)(x ) (f g)(x ) (fg )(x ) f (x ) g

15 the functionsf (x ) x 5 8 Given andg(x ) x 9 find the domain of each of the following:

(f g)(x ) (f g)(x ) (fg )(x ) f (x ) g

For the functions f(x) and g(x) are given in the graph below. Find the indicated corresponding function values (f g)(1) (f g)( 3)

Given the functionsf (x ) 6x 9 2 and g(x ) 3 x find each of each of the following: (f g)( 2) ( g f )( 2) 1

Given the functions f (x ) x and g(x ) 7x following: (f g)(x ) ( g f )(x )

(f f )(x ) 6 find each of the 1 Given the functions f (x ) x

and g(x ) 7x 6 find the domain of each of the following: (f g)(x ) ( g f )(x ) (f f )(x )

For the functions f(x) and g(x) are given in the graph below. Find the indicated corresponding function values f ( g( 3)) g(f (2))

2 Express the functionh(x ) (x 5) 2 in the form f g . If f (x ) x , find g(x). A spherical weather balloon is being inflated. The radius

of the balloon is increasing at the rate of 9 cm per second. Express the surface area of the balloon as a function of time t (in seconds).

## Recently Viewed Presentations

• Because there is no single "gold standard" for measuring gender norms, gender attitudes, women's empowerment, and other aspects of gender, we often use multiple measures. Using a single measure is not possible because gender operates in multiple spheres and has...
• INCA SUMMER SCHOOL 2005 + = LINKING THE BUDGET AND IDP INTRODUCTION The Integrated development Plan (IDP) is a strategic document that clearly outlines the city's development objectives and provides a policy framework that guides management in decision making related...
• Cathie Quinn, Heather Robertson, Eileen Blackwood, Annette McLeod, Louise Ogilvy, Bill Wright, Judith Shepherd, Hagop Bessos, Scott Wilson. 7) Election of Hon Chair - David Adams. 8) Election of Hon Vice-Chair - Patrick Mark. 9) Any other competent business -...
• If students have a better ability to make it to school than their learning ability will increase greatly and boost the graduation rates. I have had the opportunity to work with some of these children through volunteering at the Boys...
• 10 Finally, my brethren, be strong in the Lord, and in the power of his might. 11 Put on the whole . armour. of God, that ye may be able to stand against the wiles of the devil. 12 For...
• High-order vs. low-order goods. High-order goods or services. required infrequently. specialized (rare) large threshold (will go out of business in a small town) large range. Low-order goods or services. required frequently. not specialized (easy to provide) Small threshold. small range
• China and USSR Pledge Financial Support to Hanoi. ... city officials gear up for a deluge of demonstrations. Mayor Richard Daley orders police to crackdown on antiwar protests. As the nation watched on television, the area around the convention erupts...
• * Typical Project Metrics Effort/time per software engineering task Errors uncovered per review hour Scheduled vs. actual milestone dates Changes (number) and their characteristics Distribution of effort on software engineering tasks Other Project Metrics Productivity Scope of Work milestones, reports,...