Points, Vectors, and Functions Exercises

Answer

• Since f(x) is 6 for every value of x, both f(x) and f(-x) are 6. This function is even. The graph confirms this: 

• Since 6≠ -6, this function is not odd.

Answer

• We have f(x) = -x and f(-x) = -(-x) = x. These values are not the same, so f(x) is not even. These values are negatives of each other, though, so we can say f(x) is odd. 

Answer

• f(x) = x³ + x⁴ and f(-x) = (-x)³ + (-x)⁴ = -x³ + x⁴. Since f(x) are f(-x) are neither the same, nor negatives of each other, this function is neither even nor odd. From the graph it looks like f(x) is trying to be even but failing. 

• Make sure to notice the bit around the origin where f(x) dips below the y-axis.

Answer

• We have f(x) = 0 and f(-x) = 0. These values are the same, so f(x) is even. These values are also negatives of each other, since 0 = -0. Therefore f(x) is also odd. Zero is such a tricky number.