Question

Which of the following are the features for the graph of the parent absolute value function? Select all that apply.

Answer 1

Answer:

The correct options are 3, 4 and 5.

Step-by-step explanation:

The parent absolute value function is defined as

$f(x)=|x|$

where, x is any real number.

The features of the parent absolute value function are :

1. $Domain=(-\infty,\infty)$

2. $Range=[0,\infty)$

3. The function decreases on the interval $(-\infty,0]$.

4. The function increases on the interval $[0,\infty)$.

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.

Answer 2

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