Graph this a) 

f

(

−

2

)

=

0

f(−2)=0

b) 

lim

⁡

x

→

−

2

−

f

(

x

)

=

4

lim 

x→−2 

−
 

 f(x)=4

c) 

lim

⁡

x

→

−

2

+

f

(

x

)

=

0

lim 

x→−2 

+
 

 f(x)=0

d) 

lim

⁡

x

→

−

2

f

(

x

)

lim 

x→−2

 f(x) does not exist.

e) 

f

(

−

4

)

=

4

f(−4)=4

f) 

lim

⁡

x

→

−

4

−

f

(

x

)

=

4

lim 

x→−4 

−
 

 f(x)=4

g) 

lim

⁡

x

→

−

4

+

f

(

x

)

=

4

lim 

x→−4 

+
 

 f(x)=4

h) 

lim

⁡

x

→

−

4

f

(

x

)

=

4

lim 

x→−4

 f(x)=4

The graph above represents the function \( f(x) \) based on the given conditions:

- \( f(-2) = 0 \), with limits:
  - \( \lim_{x \to -2^-} f(x) = 4 \)
  - \( \lim_{x \to -2^+} f(x) = 0 \)
  - \( \lim_{x \to -2} f(x) \) does not exist due to a jump discontinuity at \( x = -2 \).

- \( f(-4) = 4 \), with limits:
  - \( \lim_{x \to -4^-} f(x) = 4 \)
  - \( \lim_{x \to -4^+} f(x) = 4 \)
  - \( \lim_{x \to -4} f(x) = 4 \), indicating a continuous point at \( x = -4 \).

Do you have any questions or need further details?

Here are 5 related questions:
1. What is the definition of a jump discontinuity?
2. How do left-hand and right-hand limits differ at a discontinuity?
3. What does it mean when a limit does not exist at a point?
4. How does continuity affect the existence of limits?
5. Can a function be discontinuous but still have limits on both sides of a point?

**Tip:** When evaluating limits, always check the left-hand and right-hand behavior of the function at the point of interest.

Graph this: a) f(-2) = 0 b) lim(x→−2−) f(x) = 4 c) lim(x→−2+) f(x) = 0 d) lim(x→−2) f(x) does not exist e) f(-4) = 4 f) lim(x→−4−) f(x) = 4 g) lim(x→−4+) f(x) = 4 h) lim(x→−4) f(x) = 4

Explore the graph of a function based on the given limits and discontinuities at x = -2 and x = -4. Learn about left-hand and right-hand limits, jump discontinuities, and continuity. Suitable for high school students in Grades 10-12.

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