Question 1

Given the graph of function $$P ($$see image 1), determine whether $$P is an $$even function, an odd function, or neither. Recall that a function $$f(x) is $$even if $$f(-x) = f(x)$$ for all $$x in $$its domain, and odd if $$f(-x) = -f(x).$$

Accepted Answer

Even

Question 2

Given the graph of function $$Q ($$see image 2), determine whether $$Q is an $$even function, an odd function, or neither.

Accepted Answer

Even

Question 3

Given the graph of function $$R ($$see image 3), determine whether $$R is an $$even function, an odd function, or neither.

Accepted Answer

Odd

Question 4

Consider the equation $$x^{\frac{4}$${5}} - $$y^{\frac{4}$${5}} = 5$$. Which type of symmetry does its graph exhibit?

Accepted Answer

Symmetric about the y-axis

Question 5

Suppose a function $$f(x) is $$even. Which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = f(x)$$

Question 6

Suppose a function $$g(x) is $$odd. Which of the following must be true for all $$x in $$the domain of $$g$$?

Accepted Answer

$$g(-x) = -g(x)$$

Question 7

A function $$h(x) is $$defined such that $$h(-x) = h(x)$$ for all $$x. $$Which of the following statements is true?

Accepted Answer

$$h(x) is an $$even function

Question 8

Consider the function $$f(x) = x^3$ - x. Is$$ $$f(x)$$ even, odd, or neither?

Accepted Answer

Odd

Question 9

Suppose a function $$f(x) is $$neither even nor odd. Which of the following could be an example of such a function?

Accepted Answer

$$f(x) = x^2$ + x$$

Question 10

A real-world scenario: The height $$h(t) of a $$bouncing ball at time $$t is $$modeled by $$h(t) = -16t^2$ + 32t + 5. Is $$this function even, odd, or neither?

Accepted Answer

Neither

Question 11

Suppose the slope of a curve is negative at points $$A$$, $$B$$, and $$D. $$Which of the following best describes where the function is decreasing?

Accepted Answer

At points $$A$$, $$B$$, and $$D$$

Question 12

Which of the following real-world functions is most likely to be even?

Accepted Answer

The temperature at a point $$x$$ miles east or west of a city center, $$T(x)$$

Question 13

Which of the following real-world functions is most likely to be odd?

Accepted Answer

The force exerted by a spring as a function of displacement, $$F(x)$$, where $$F(x) = -kx$$

Question 14

If a function $$f(x) is $$even and $$f(3) = 7$$, what is $$f(-3)$$?

Accepted Answer

$$7$$

Question 15

If a function $$g(x) is $$odd and $$g(2) = -5$$, what is $$g(-2)$$?

Accepted Answer

$$5$$

Properties of Functions: Even, Odd, or Neither

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