Exploring Even and Odd Functions

What is one of the objectives of today's lesson?

• Learning to solve quadratic equations

• Exploring the properties of logarithms

• Determining even and odd functions from graphs

• Understanding the Pythagorean theorem

What is the defining characteristic of an even function?

• It is symmetric with respect to the x-axis

• It is symmetric with respect to the origin

• It is symmetric with respect to the y-axis

• It has no symmetry

Which of the following is an example of an odd function?

• y = x^3

• y = x^2

• y = x + 1

• y = |x|

How can you determine if a function is even or odd from its equation?

• By plugging in positive x values

• By finding the derivative of the function

• By checking if the function is continuous

• By plugging in negative x values and comparing results

What happens when you plug a negative x value into an even function?

• You get a different y value

• You get the same y value

• You get a negative y value

• The function becomes undefined

What does it mean for a function to be increasing on an interval?

• The function's y values are increasing

• The function's y values are constant

• The function's x values are decreasing

• The function's y values are decreasing

In interval notation, how would you represent a function that is decreasing from x = -6 to x = -4?

• [-6, -4)

• [-6, -4]

• (-6, -4)

• (-6, -4]

What is a local maximum on a graph?

• A point where the function's value is the highest in its vicinity

• A point where the function's value is constant

• A point where the function's value is the lowest in its vicinity

• A point where the function's value is undefined

Where does a local minimum occur on a graph?

• At a valley

• At a peak

• At the origin

• At a point of inflection

What is the interval on which the function is increasing if it goes up from x = -2 to x = 0?

• (-2, 0)

• (-2, 2)

• (0, 2)

• (-2, -1)