# Functions, Graphs, and Limits

# Graphing and Visualizing Limits Exercises

### Example 1

Let *y* = *f*(*x*) = sin(*x*). What is the limit of *f*(*x*) as *x* approaches:

*0*?

### Example 2

Let *y* = *f*(*x*) = sin(*x*). What is the limit of *f*(*x*) as *x* approaches:

- 2π?

### Example 3

Let *y* = *f*(*x*) = sin(*x*). What is the limit of *f*(*x*) as *x* approaches:

- π / 2?

### Example 4

Let *y* = *f*(*x*) = sin(*x*). What is the limit of *f*(*x*) as *x* approaches:

- -π?

### Example 5

Let *f*(*x*) = *x*^{2} -4*x* + 3. Graph *f*(*x*) and use the graph to find the limit of *f*(*x*) as *x* approaches...

- 0

### Example 6

Let *f*(*x*) = *x*^{2} -4*x* + 3. Graph *f*(*x*) and use the graph to find the limit of *f*(*x*) as *x* approaches...

- 3

### Example 7

Let *f*(*x*) =* x*^{2} -4*x* + 3. Graph *f*(*x*) and use the graph to find the limit of *f*(*x*) as *x* approaches...

- 1

### Example 8

Although we say "the limit of *f*(*x*) as *x* approaches 2 is 5," we write

lim_{x to 2 }*f*(*x*) = 5.

Let *f*(*x*) = 2 - 2*x*. Find the limit.

- lim
_{x to 2}*f*(*x*)

### Example 9

Let *f*(*x*) = 2 - 2*x*. Find the limit.

- lim
_{x to 0 }*f*(*x*)

### Example 10

Let *f*(*x*) = 2 - 2x. Find the limit.

- lim
_{x to 1 }*f*(*x*)