Question 1

Given the point $$(3, -5)$$, which of the following is its symmetric point with respect to the origin?

Accepted Answer

$$(-3, 5)$$

Question 2

Which of the following functions is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$f(x) = x^2$

Question 3

If $$f(x) is an $$odd function, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

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

Question 4

Given $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of f(x) - g(x$$)$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 5

Which of the following graphs represents a function with symmetry about the $$x-$$axis?

Accepted Answer

A graph of $$y^2 = x$

Question 6

If $$f(x) is $$defined for $$x = -2, -1, 0, 1, 2$$ and $$g(x) is $$defined for $$x = -1, 0, 1, 2, 3$$, what is the domain of $$f(x) - g(x)$$?

Accepted Answer

$$x = -1, 0, 1, 2$$

Question 7

Which of the following points is symmetric to $$(3, -5)$$ with respect to the $$x-$$axis?

Accepted Answer

$$(3, 5)$$

Question 8

A function $$f(x) is $$said to have symmetry about the origin if:

Accepted Answer

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

Question 9

Which of the following is NOT a possible domain for the difference of two functions $$f$$ and $$g$$?

Accepted Answer

The union of the domains of $$f$$ and $$g$$

Question 10

If a function $$f is $$symmetric with respect to the $$y-$$axis, which of the following must be true?

Accepted Answer

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

Question 11

Which of the following functions is symmetric about the origin?

Accepted Answer

$$f(x) = x^3$

Question 12

Given the point $$(3, -5)$$, which of the following is its symmetric point with respect to the $$y-$$axis?

Accepted Answer

$$(-3, -5)$$

Question 13

Which of the following is true about the graph of $$y = x^2$?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 14

If $$f(x) is $$defined only for $$x = -2, -1, 0, 1, 2$$ and $$g(x) is $$defined only for $$x = 0, 1, 2, 3, 4$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$x = 0, 1, 2$$

Question 15

Which of the following is a function that is symmetric about both the $$x-$$axis and $$y-$$axis?

Accepted Answer

$$y^2$$ = $$x^2$$

Functions, Domains, and Symmetry in College Algebra

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