Question

Consider this function and its graph. f(x) = tan(3x + pi/4) - 1 Which statement best describes function f?

A. The function is odd.
B. The function is even.
C. There is not enough information to determine whether the function is even or odd.
D. The function is neither even nor odd.

Answer 1

D. The function is neither even nor odd

Explanation:

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Answer 2

Answer: D. The function is neither even nor odd.

Explanation:

A function f(x) is even if:

f(x) = f(-x) for all x-valies

A function f(x) is odd if:

f(x) = -f(-x) for all x-values.

If there is only one value of x such that the above conditions are false, then the function is neither odd nor even.

In the graph, we can see that:

f( -π/3) = f(π/3)

This would imply that the function is even (at least in that point)

And can also see that as x increases from zero, the value of f(x) increases.

And as x decreases from zero, the graph of f(x) decreases.

So for a point 1 > a > 0, we have that:

f(a) ≠ f(-a)

Then we can conclude that the function is neither even nor odd, the correct option is D.