Question 1

Which algebraic test determines if a graph is symmetric with respect to the y-axis?

Accepted Answer

Replace $$x$$ with $$-x$$ and check if the equation is equivalent.

Question 2

Given the equation $$y^2$$ = $$3x^2$$, which symmetry does its graph exhibit?

Accepted Answer

Symmetric with respect to both the x-axis and y-axis

Question 3

If the point $$(-10, -7) is $$reflected across the y-axis, what is the resulting point?

Accepted Answer

$$(10, -7)$$

Question 4

A function $$f is $$called even if:

Accepted Answer

$$f(x) = f(-x)$$ for all $$x in $$the domain

Question 5

Which of the following statements is true for an odd function?

Accepted Answer

Its graph is symmetric with respect to the origin.

Question 6

Given $$f(x) = 4x^2$ - 7x + 3$$, determine whether $$f is $$even, odd, or neither.

Accepted Answer

Neither

Question 7

If the point $$(-10, -7) is $$reflected across the origin, what is the resulting point?

Accepted Answer

$$(10, 7)$$

Question 8

Which of the following equations is symmetric with respect to the x-axis?

Accepted Answer

$$y^2 = x$

Question 9

A chemical reaction is modeled by $$y = x^3$. What type of symmetry does this function have?

Accepted Answer

Symmetric with respect to the origin

Question 10

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

Accepted Answer

$$-5$$

Question 11

Suppose $$f(x) = x^2$ + 1. Is$$ $$f$$ even, odd, or neither?

Accepted Answer

Even

Question 12

Which of the following is NOT a correct algebraic test for symmetry?

Accepted Answer

Replace $$x$$ with $$y$$ for y-axis symmetry.

Question 13

A medical dosage curve is modeled by $$y = x^4$. What type of symmetry does this function have?

Accepted Answer

Symmetric with respect to the y-axis

Question 14

If $$f(x) is $$even and $$f(3) = 8$$, what is $$f(-3)$$?

Accepted Answer

$$8$$

Question 15

Which of the following points is symmetric to $$(4, -5)$$ with respect to the x-axis?

Accepted Answer

$$(4, 5)$$

Question 16

A function $$f(x) is $$defined as $$f(x) = x^3$ + x. Is$$ $$f$$ even, odd, or neither?

Accepted Answer

Odd

Question 17

If a graph is symmetric with respect to the origin, which of the following must be true?

Accepted Answer

If $$(x, y) is on $$the graph, so is $$(-x, -y).$$

Question 18

Which equation is symmetric with respect to the origin?

Accepted Answer

$$y = x^3$

Question 19

A real-world scenario: The height of a projectile is modeled by $$h(t) = -t^2$ + 10t. Is $$this function even, odd, or neither?

Accepted Answer

Neither

Question 20

If $$f(x) = x^2$ - 4$$, what is $$f(-x)$$?

Accepted Answer

$$x^2 - 4$

Symmetry of Graphs and Even/Odd Functions

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