# EVALUATING LIMITS OF LIMITS FROM GRAPH

Give the value of each statement. If the value does not exist, write "does not exist" or "undefined".

Evaluate the following from the graph given below. Problem 1 :

lim x→−1- f(x)

Solution : Approaching -1 from left side, we get the value of y as 3. So,

lim x→-1-  f(x) = 3

Problem 2 :

f(1) Solution :

We see the filled circle at (1, 1). So, the value of f(1) is 1.

Problem 3 :

lim x→0 f(x) Solution :

At exactly x approaches 0, the output is 0.

lim x→0 f(x) = 0.

Problem 4 :

lim x→2+ f(x) Solution : Approaching 2 from right side, the output is 1.

So, lim x→2+ f(x) = 1

Problem 5 :

f(-1)

Solution :

We see the filled circle at (-1, 1). So, the value of f(-1) is 1.

Problem 6 :

f(2)

Solution :

f(2) = does not exists.

Problem 7 :

lim x→−1+ f(x)

Solution : Approaching -1 from right side, we get the value of y as 1. So,

lim x→-1+  f(x) = 1

Problem 8 :

lim x→1- f(x)

Solution : Approaching 1 from left side, we get the value of y as -1. So,

lim x→1 f(x) = -1

Problem 9 :

lim x→2 f(x)

Solution :

Both left hand and right hand limits are not equal, the limit does not exists at x = 2.

lim x→2  f(x) = DNE

Evaluate the following from the graph given below. Problem 1 :

lim x→-3 f(x)

Solution :

lim x →-3 f(x)

At x = -3, the curve touches the x-axis. So, the output is 0.

lim x →-3 f(x) = 0

Problem 2 :

f(1) Solution :

The point f(1) does not pass through any points. So, the answer is does not exists.

Problem 3 :

lim x→1 f(x) Solution :

Left  hand limits are not equal. Then right hand limit is exists at x = 1.

lim x→1 f(x) = -5

Problem 4 :

lim x→-2+  f(x) Solution :

Approaching -2 from right side, we get the value of y as 4. So,

lim x→-2 f(x) = 4

Problem 5 :

f(3)

Solution :

The curve passes through the point (3, -1).

f(3) = -1

Problem 6 :

lim x→-2-f(x)

Solution :

Approaching -2 from left side, we get the value of y as 1. So,

lim x →-2-  f(x) = 1

Problem 7 :

lim x→-2  f(x)

Solution :

Both left hand and right hand limits are not equal, the limit does not exists at x = -2.

lim x→-2  f(x) = DNE

Problem 8 :

f(-2)

Solution :

We see the filled circle at (-2, 3). So, the value of f(-2) is 3.

Problem 9 :

f(4)

Solution :

The curve passes through the point (4, 1), so the value of f(4) is 1.

Evaluate the following from the graph given below.

Problem 1 :

lim x→3+ f(x) Solution : Approaching 3 from right side, we get the value of y as 1. So,

lim x→3+  f(x) = 1

Problem 2 :

f(3)

Solution :

The curve does not pass through any points on the y-axis. So, the answer is does not exists.

Problem 3 :

lim x→0 f(x) Solution :

At exactly x approaches 0, the output is 1.

lim x→0 f(x) = 1.

Problem 4 :

lim x→3 f(x) Solution :

Both left hand and right hand limits are not equal, the limit does not exists at x = 3.

lim x→3  f(x) = DNE

Problem 5 :

f(0)

Solution :

The curve is passing through (0, 2). So, the value of f(0) is 2.

Problem 6 :

lim x→3- f(x) Solution : Approaching 3 from right side, we get the value of y as -2. So,

lim x→3-  f(x) = -2

Problem 7 :

lim x→0+ f(x)

Solution :

While approaching the value 0 from left side, the output becomes 1.

So, lim x→0+ f(x) = 1.

Problem 8 :

f(1)

Solution :

The curve is passing through (1, 0). So, the value of f(1) is 0.

## Recent Articles 1. ### Solving Direct and Inverse Proportion Word Problems Worksheet

Sep 22, 23 08:41 AM

Solving Direct and Inverse Proportion Word Problems Worksheet

2. ### Round the Decimals to the Nearest Indicated Place Value

Sep 22, 23 06:13 AM

Round the Decimals to the Nearest Indicated Place Value