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Function Operations (Composite Functions)

Total questions: 20

Worksheet time: 45mins

Name
Class
Date
1.
f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x). 
a)
14x-10
b)
-8x+2
c)
2x+2
d)
2x-2
2.
f(x) = x2+9
g(x) = x-9
Find f(x)-g(x). 
a)
x2+x+9
b)
x2-x+9
c)
x2-x
d)
x2-x+18
3.
f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)
a)
4x2+24
b)
4x2+20x+24
c)
4x2+12x+24
d)
4x2+4x+24
4.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))
a)
16
b)
4
c)
-4
d)
None of these.
5.
All of the x values or inputs are called what?
a)
Domain
b)
Range
c)
Relation
d)
Function
6.
p(x) = 3x + 4
q(x) = 2x2
Find q(p(-2))
a)
8
b)
-8
c)
28
d)
None of these.
7.
a)
9 - 8/3
b)
9 + 8/3
c)
3
d)
1/3
8.

f(x) = 3x + 10

g(x) = x - 2


Find (f∘g)(0)

(a)  

9.
Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
10.

What are the domain restrictions f(x)=3x2+6x+5f\left(x\right)=\frac{3}{x^2+6x+5}

a)

x≠−5,−1x\ne-5,-1  

b)

x≠1,5x\ne1,5  

c)

x>5, x<1x>5,\ x<1  

d)

x<−5, x>−1x<-5,\ x>-1  

11-13.

Understanding Composite Functions in Algebra

A composite function in algebra is a combination of two functions where the output of one function becomes the input of another. This concept is essential in understanding more complex mathematical operations.

When defining a composite function, it is denoted as (f ∘ g)(x), where f and g are the two functions being combined. The order in which the functions are composed is crucial, as changing the order can result in different outcomes.

Composite functions are commonly used in various fields such as physics, engineering, and computer science to model real-world phenomena and solve complex problems. Understanding how to work with composite functions is a fundamental skill for students studying algebra.

By mastering the concept of composite functions, students can enhance their problem-solving abilities and gain a deeper understanding of the relationships between different mathematical functions. Practice and application of composite functions can help students excel in algebra and other advanced mathematical subjects.

11.

Why is understanding composite functions essential for students studying algebra?

a)

It helps in developing problem-solving skills

b)

It deepens the understanding of mathematical relationships

c)

It is a requirement for passing algebra exams

d)

It is not important for algebra students

12.

Why are composite functions crucial for understanding complex mathematical operations?

a)

They simplify the process of solving equations

b)

They combine two functions to create a new function

c)

They are only used in basic arithmetic

d)

They are not relevant in algebra

13.

Why is the order of composition important in composite functions?

a)

It affects the domain and range of the composite function (can result in different outcome).

b)

It changes the value of the composite function

c)

It determines the input and output of the composite function

d)

It has no impact on the composite function

14.
What is the proper way to write the answer for the following problem? 
a)
2x3-x2-25x-12
b)
2x4-x3-25x2-12x+0
15.

What the remainder after x2 - x - 6 is divided by x - 3

(a)  

16.

Determine if the binomial is a factor of the polynomial. (Apply Remainder Theorem)

(3n3−26n2−39n−10)÷(n−10)\left(3n^3-26n^2-39n-10\right)\div\left(n-10\right)  

a)

Yes

b)

No

17.
Based on the end behavior of the polynomial, what best describes the leading coefficient?
a)
a negative real number
b)
 a positive real number
c)
an even real number
d)
an odd real number
18.
What are the linear terms of the polynomial function?
a)
(x-2)(x-1)(x+1)(x-2)
b)
(x-2)(x-1)(x+1)(x+2)
c)
(x-2)(x-1)(x+1)(x+2)(x-4)
d)
(x-2)(x-1)(x+1)(x+2)(x+4)
19.
Classify the polynomial by degree.
a)
quartic
b)
quintic
c)
6th degree polynomial 
d)
7th degree polynomial
20.
The degree of the polynomial determines the number of roots.
a)
True
b)
False
21.
What is the end behavior as x → -∞ f(x)→ ?
a)
-∞
b)
∞
22.

Given the function f(x) = x3 - 6x2 + 11x - 6, what is f(2)?

a)

1

b)

0

c)

-1

d)

2