Question

The function shown is reflected across the y-axis tocreate a new function.4-321-5-4-3-2-11- 12345 xAYRIS++Which is true about the domain and range of eachfunction?O Both the domain and range change.Both the range and domain stay the same.O The domain stays the same, but the range changes.O The range stays the same, but the domain changes.

Answer 1

Step-by-step explanation

To answer this question, we take into account the following definitions:

• The ,domain, of a function is the complete set of possible values of the independent variable (x, usually).

,

• The ,range, of a function is the complete set of all possible resulting values of the dependent variable (y, usually) after we have substituted the domain.

Reflecting the function across the y-axis gives the following graph:

Where the blue graph is the original function, and the red graph is the reflected function.

From this graph, we see that:

• both functions are defined for all the real numbers ⇒ their domain is (-∞, ∞),

,

• both functions take values in the interval (-∞, -1] ⇒ their range is (-∞, -1],

We conclude that after the reflection, both functions have the same domain and range.

Answer

Both the range and domain stay the same.