Question

For which interval is the function constant?

(4, ∞)
(0, 4)
(−4, 0)
(−∞, −4)

Answer 1

The interval from x = -4 to x = 0 is when the graph is completely flat.

We can write this interval as -4 < x < 0 which becomes (-4,0) in interval notation

That's why the answer is choice C

Note: be careful not to mix up interval notation and ordered pair notation

Answer 2

The interval in which the function is constant is:

(-4,0)

Explanation:

A function is constant if it has the same output value for the every input value.

Also, the graph of a constant function is a horizontal line i.e. a line with zero slope ( i.e. y=a for some 'a' )

Now in the given graph we observe that the graph:

• is a decreasing function in the interval (-∞,-4).

( since it is a line with negative slope )

• is a horizontal line in the interval (-4,0).

• is a decreasing function in the interval (0,4) .

( Since the graph is a line with negative slope )

• and is a increasing function in the interval (4,∞).

( Since the graph is a line with positive slope )

Hence, the interval in which the function is constant is:

(-4,0)