Select the vertical asymptote(s) of the following function:

Question

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2 points
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y = 0
y = 1
y = -1
x = -3
x = 3
x = 0
What is the Horizontal Asymptote of the following function.
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2 points
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x = -4
x = -2
x = 0
x = 2
y = -4
y = -2
y = 0
y = 2
Where is the point of discontinuity located for the function below?
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2 points
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x = -16
x = -4
x = 4
x = 15
There is no point of discontinuity
Select the horizontal asymptote(s) of the following function:
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2 points
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y = 0
y = 1
y = -1
x = -3
x = 3
x = 0
If a graph is symmetrical about the y-axis, then it is
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2 points
even
odd
neither
What is the Vertical Asymptotes of the following function.
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2 points
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x = -4
x = -2
x = 0
x = 2
y = -4
y = -2
y = 0
y = 2
Determine whether the following function is Even, Odd, or Neither
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2 points
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Even
Odd
Neither
Identify the equation of the function.
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2 points
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y = - (x + 2)^2 + 4
y = - (x - 2)^2 + 4
y = - (x + 4)^2 + 2
y = -2|x + 2| + 4
Last Name
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First Name
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If a graph is symmetrical about the origin, then it is
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2 points
even
odd
neither
What type of translation is the following function?
g(x) = -3|x + 1| - 5
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2 points
3 up
3 down
5 up
5 down

Answer 1

To address each of your questions, I will provide the answers based on typical function behaviors and characteristics. However, without visual references, please ensure to validate these answers with the actual functions or graphs in question.

1. Vertical Asymptote(s):
   Without the specific function, typically, vertical asymptotes occur where the function approaches infinity or negative infinity. Common values provided that could represent vertical asymptotes are:

   • x = -3
   • x = 3
   • x = 0

   The correct selections would depend on the function's behavior in relation to these values.

2. Horizontal Asymptote:
   Similar to vertical asymptotes, horizontal asymptotes describe the behavior of the function as x approaches infinity or negative infinity. Possible answers could be:

   • y = -4
   • y = -2
   • y = 0
   • y = 2

   Look for the function's leading coefficients or end behavior to determine the horizontal asymptote.

3. Point of Discontinuity:
   Discontinuities can occur at values where the function is not defined. Your options are:

   • x = -16
   • x = -4
   • x = 4
   • x = 15
   • There is no point of discontinuity.

   Identify where the function is undefined or jumps.

4. Horizontal Asymptote(s):
   This is a repeat question from the second one, so it would be answered in the same way.

5. Symmetry about the y-axis:
   A function is even if it satisfies \( f(-x) = f(x) \) for all x in its domain. Therefore, if a graph is symmetrical about the y-axis, it is:

   • Even.

6. Vertical Asymptotes:
   Again, without specific details about the function, potential vertical asymptotes would usually include:

   • x = -4
   • x = -2
   • x = 0
   • x = 2

   You would determine this based on where the function is undefined.

7. Even, Odd, or Neither:
   A function is odd if it satisfies \( f(-x) = -f(x) \), and neither if it does not satisfy the conditions for either. This again depends on the function characteristics provided.

8. Identify the equation of the function:
   Without knowing the behavior of the graph functions listed:

   • Look for vertex form or transformations associated with parabola/absolute value functions, and relate your choices accordingly.

9. Symmetry about the origin:
   A function is odd if it is symmetrical around the origin. Thus, if it shows this symmetry, it is:

   • Odd.

10. Translation type of the function:
    The function \( g(x) = -3|x + 1| - 5 \) indicates transformations:

    • The negative sign indicates a reflection, the term \(-5\) translates the graph 5 units downwards. The function thus represents a vertical shift. So:
    • 5 down.

Please ensure the answers match what you see on your graphs and functions, as I rely on typical characteristics for interpretations.