Which of the following are the features for the graph of the parent absolute value function? Select all that apply.
1. The domain is [0,sideways 8).
2. The range (- sideways 8,sideways 8).
3. The function decreases on the interval (- sideways 8, 0).
4. The function is even. 5. The function is continuous.

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tramserran tramserran · Answer 1 · 2018-09-24T05:13:54+02:00

absolute value graph looks like a V, with the vertex at the origin.

1. the domain (x-values) is: (∞, ∞) TRUE

2. the range (y-values) starts at the vertex: [0, ∞) FALSE

3. the function decreases when left of vertex and increases when right of vertex: decreases (-∞, 0) TRUE

4. f(x) = |x| = +/-x

f(-x) = |-x| = +/-x

f(x) = f(-x) so the function is even TRUE

5. every x-value has a corresponding y-value (there are no gaps) so the function is continuous. TRUE

Answers: 1, 3, 4, 5

erinna erinna · Answer 2 · 2019-10-20T07:56:16+02:00

Answer:

The correct options are 3, 4 and 5.

Step-by-step explanation:

The parent absolute value function is defined as

[tex]f(x)=|x|[/tex]

where, x is any real number.

The features of the parent absolute value function are :

1. [tex]Domain=(-\infty,\infty)[/tex]

2. [tex]Range=[0,\infty)[/tex]

3. The function decreases on the interval [tex](-\infty,0][/tex].

4. The function increases on the interval [tex][0,\infty)[/tex].

5. The function is even because f(-x)=f(x) for any value of x.

6. The graph of an absolute value function is a V-shaped unbroken curve. So, it is a continuous function.

From the above features we can say that the options 3, 4 and 5 are correct.