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Function Symmetry and Characteristics

Function Symmetry and Characteristics

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to determine if a function is odd, even, or neither. It describes that a function is even if f(-x) equals f(x) and odd if f(-x) equals -f(x). The tutorial uses the function f(x) = x^2 + 2x - 3 as an example, showing that it is neither odd nor even. Graphical representations are discussed, highlighting that even functions are symmetric with the y-axis and odd functions with the origin. The video concludes by confirming the example function's lack of symmetry.

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in determining if a function is odd, even, or neither?

Graph the function.

Find the derivative of the function.

Substitute -x into the function.

Check if the function is linear.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a key characteristic of an even function?

It is symmetric with the y-axis.

It is not symmetric at all.

It is symmetric with the origin.

It is symmetric with the x-axis.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens when you substitute -x into an odd function?

You get a constant value.

The function becomes undefined.

You get the negative of the original function.

You get the original function.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the given example function in the video?

f(x) = x^3 - 3x + 2

f(x) = x^2 - 2x + 3

f(x) = x^3 + 3x - 2

f(x) = x^2 + 2x - 3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of substituting -x into the example function f(x) = x^2 + 2x - 3?

-x^2 + 2x + 3

x^2 - 2x - 3

x^2 + 2x - 3

-x^2 - 2x + 3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the example function neither odd nor even?

It is symmetric with the x-axis.

It is symmetric with both axes.

It is not symmetric with the y-axis or the origin.

It is a linear function.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does an even function's graph look like?

Symmetric with the origin

Symmetric with the y-axis

Not symmetric at all

Symmetric with the x-axis

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