Question

Select the vertical asymptote(s) of the following function:
*
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.
*
2 points
Captionless Image
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?
*
2 points
Captionless Image
x = -16
x = -4
x = 4
x = 15
There is no point of discontinuity
Select the horizontal asymptote(s) of the following function:
*
2 points
Captionless Image
y = 0
y = 1
y = -1
x = -3
x = 3
x = 0
If a graph is symmetrical about the y-axis, then it is
*
2 points
even
odd
neither
What is the Vertical Asymptotes of the following function.
*
2 points
Captionless Image
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
*
2 points
Captionless Image
Even
Odd
Neither
Identify the equation of the function.
*
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
*
First Name
*
If a graph is symmetrical about the origin, then it is
*
2 points
even
odd
neither
What type of translation is the following function?
g(x) = -3|x + 1| - 5
*
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.