Q3 Determine algebraically whether the function is even odd

Q3. Determine algebraically whether the function is even, odd, or neither.

f(x) = 2x³
   a. even
   b. odd
   c. neither

Q4. Answer the question about the given function.

Given the function f(x) = -7x² + 14x + 4, if x = 1, what is f(x)? What point is on the graph of f?
   a. 11; (1, 11)
   b. 11; (11, 1)
   c. -17; (1, -17)
   d. -17; (-17, 1)

Solution

Q 3. We know that a real-valued function f(x) of a real variable x is even if f(x) = f(-x) for all x and -x in the domain of f . Also, f is odd if f (-x) = - f(x) for all x and -x in the domain of f. Here, f(x) = 2x³ so that f(-x) = 2(-x)³ = -2x³ = -f(x). Thus, f(x) = 2x³ is an odd function. The answer b is correct.

Q 4. We f(x) = -7x² + 14x + 4 so that , if x is 1, then f(x) = f(1) = -7(1)² + 14(1) + 4 = -7+14 + 4 = 11 . Thus, the point (1,11) is on the graph of F9x). The answer a is correct.