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).