Limits(Piecewise and review)

Piecewise Functions

and Function Notation

Piecewise Functions

• Remember to look at the inequality symbols for open or closed circles and to see which way to connect the dots.

• You also need to look here for function notation.

• f(0) = -4 and f(2) = 1

Multiple Choice

What is f when x equals 4?

• -5
• 0
• 3
• 6

Multiple Choice

What is the limit of h(x) as x approaches -4?

• $$16$$

• $$4$$

• $$-4$$

• $$DNE$$

​**Copy these Notes on your paper on this slide!!

​Find f(-3).

​Solution: Determine which domain -3 falls within. In this case, it falls within the first piece's domain since -3 is less than -1. Therefore, we use the equation -x+1.

​Plug in -3 in place of the x and simplify.

​f(-3) = - (-3) +1

​ = 3+1

​f(-3)= 4 The answer is 4.

​**Copy these Notes on your paper on this slide!!

​Find f(4).

​Solution: Determine which domain 4 falls within. In this case, it falls within the second piece's domain since 4 is greater than -1. Therefore, we use the equation 2x.

​Plug in 4 in place of the x and simplify.

​f(4) =2 (4)

​ ​f(4)= 8 The answer is 8.

Multiple Choice

What is g(7) if:

• -17

• -13 

• 13       

• 17

Multiple Choice

What is f(-2)?

• 4

• 1

• 1

• DNE

Multiple Choice

What is m(-3) if:    

• -3

• 0.5

• 3

• -3.5

Fill in the Blanks

Find f(-3) =

Fill in the Blanks

Find f(0) =

Fill in the Blanks

Find f(2) =

Fill in the Blanks

Find f(5) =

Multiple Choice

Find f(-2)

• -3
• 6
• 8
• -6

Multiple Choice

$$\lim_{x\rightarrow3}\ \ \frac{x^2+2x-15}{x^2-x-6}\ =\ ....$$  

• $$\frac{5}{8}$$  

• $$\frac{8}{5}$$  

• $$-\frac{8}{5}$$  

• $$-\frac{5}{8}$$  

• 0

Multiple Choice

Find the limit. Hint: Where is the horizontal asymptote?

• ³/₇

• 0

• ∞

• -∞

Multiple Choice

Find the limit. Hint: Where is the horizontal asymptote?

• ^-2/₉

• 0

• ∞

• -∞

Multiple Choice

$$\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}$$  

• 0

• DNE

• 1/2

• 2

Multiple Choice

$$\lim_{x\rightarrow-2}\left(\frac{x+2}{x^2+5x+6}\right)$$  

• ∞
• 0

• 3
• 1

Multiple Choice

$$\lim_{x\rightarrow1}\ \left(-\frac{x-1}{x^2+2x-3}\right)$$  

• -1/4
• 8
• 0

• ∞

Multiple Choice

Given the value of f(x), find $$\lim_{x\rightarrow2}\ f\left(x\right)$$  

• -1
• -4
• 8
• 5

Multiple Choice

What is the  $$\lim_{x\rightarrow2}f\left(x\right)$$ ?

• 1

• 2

• 0

• does not exist

Multiple Choice

Based on the graph, evaluate f(-1) .

• undefined

• -1

• -1

• 3

Multiple Choice

What is the  $$\lim_{x\rightarrow2}\frac{x^2\ -6x\ +8}{2x\ -\ 4}$$  ?

• 2

• -2

• -1

• does not exist