Final Exam Review: Unit 1 (Functions)

• State the domain and range from a graph

• Add, subtract, multiply, and divide functions

• Find the composition of functions given an equation, table, or graph

• Simplify the difference quotient for a given function

​unit 1: Functions

​Domain restrictions

1. You cannot divide by zero.

2. You cannot take an even root of a negative number.

3. You cannot take the log of a negative number.

Multiple Choice

$$\frac{3}{x+4}$$  What is the restricted domain?

• $$x\ge4$$  

• $$x\ge3$$  

• $$x\ne3$$  

• $$x\ne-4$$  

Multiple Choice

$$\frac{5}{\sqrt{x-2}}$$  Choose the domain for which the function is defined.

• $$x\ne2$$  

• $$x\ne5$$  

• $$x>2$$  

• $$x\ge5$$  

Multiple Choice

What are the domain restrictions of $$f\left(x\right)=\frac{x+3}{x^2-16}$$  ?

• $$x\ne4,-4$$  

• $$x\ne0$$  

• $$x\ge16$$  

• $$\left(-4,4\right)$$  

Multiple Choice

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

• $$x\ne-5,-1$$  

• $$x\ne1,5$$  

• $$x>5,\ x<1$$  

• $$x<-5,\ x>-1$$  

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Multiple Choice

what is f(g(2))

• 6

• 4

• 3

• None of the Above

The Difference Quotient

Multiple Choice

Find the difference quotient when f(x) = x² - x + 1

• 2x - 1 + h
• 4x - 5 - h
• -2x - 1 + h 
• x² + 2h