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Aleks [24]
3 years ago
11

Stephon makes the following statements: statement 1 lim x -3 f(x) exists and is equal to 1 statement 2 lim x 1 f(x) exists and i

s equal to 1

Mathematics
1 answer:
Mandarinka [93]3 years ago
4 0

Neither statement 1, nor statement 2 are correct

The given Stephon's statements are;

Statement 1; \mathbf{\lim \limits  _{x \to -3} f(x)}  \ \mathbf{Exist} \ and \mathbf{\lim \limits  _{x \to -3} f(x) = 1}

Statement 2; \mathbf{\lim \limits  _{x \to 1} f(x)}  \ \mathbf{Exist} \ and \mathbf{\lim \limits  _{x \to 1} f(x) = 1}

The analysis of the graph and reason for the answer

From the graphed line on the left of the y-axis, we have an open circle at x = -3, and an arrow at the other end pointing towards negative infinity, (-∞) which indicates that the domain is -∞ ≤ x < -3, therefore, at x = -3, f(x) does not exist, therefore, we can write the following statement

The limits of the domain and range of the graph includes;

\mathbf{\lim \limits  _{x \to -3} f(x)} = \mathbf{Does \ not \ exist}

f(x) = Defined for -∞ ≤ x < -3

Similarly, from the graphed line on the right of the y-axis, we have an open circle at x = 1 and an arrow at the other end of the line f(x) = 4 pointing towards positive (+∞) infinity, which indicates the domain and the graph of the function is 1 < x ≤ ∞ , therefore, f(x) does not exist at x = 1, and we can write

\mathbf{\lim \limits  _{x \to 1} f(x)} = \mathbf{Does \ not \ exist}

From we above, we have that neither statement 1, nor statement 2 are correct

Learn more about open and closed circles on graph lines

brainly.com/question/8648835

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