Question

Select all the correct answers. Which functions have a range of {y ε R [-[infinity] < y < [infinity]]}?

A. Linear functions
B. Exponential functions
C. Quadratic functions
D. Trigonometric functions

Answer 1

The functions with a range of all real numbers are linear functions (A) and, considering the tangent function, trigonometric functions (D).

Step-by-step explanation:

The question asks which functions have a range where y can take on any real value from negative infinity to positive infinity (y ∈ R [-∞ < y < ∞]). The correct answers are:

• A. Linear functions: The graph of any non-vertical linear function is a line that extends indefinitely in both the positive and negative y-directions, thus having a range of all real numbers.
• D. Trigonometric functions: While an individual trigonometric function like sine or cosine does not have a range of all real numbers, the general category of trigonometric functions includes the tangent function, which does have a range of all real numbers.

So, the correct selections are A (Linear functions) and D (Trigonometric functions).