Analyzing Function Behavior and Parameters

Analyzing Function Behavior and Parameters

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explores the concept of families of functions, focusing on how individual functions within a family share common features but differ based on parameters. It uses the example of a function f(x) = ax/(x^2 + B) to illustrate how parameters A and B affect the graph's shape, critical points, and behavior. The tutorial also discusses the impact of positive and negative values for these parameters and how to design a function with specific characteristics, such as a peak at a certain point.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary focus when analyzing individual functions using derivatives?

To determine the function's domain

To calculate the function's range

To understand the behavior of the function

To find the maximum value of the function

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a family of functions?

Functions with the same domain

Functions that share common features

A set of unrelated functions

Functions with identical graphs

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function f(x) = ax / (x^2 + B), what role do A and B play?

They are variables

They are roots of the function

They are coefficients of x

They are constants that define the family

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the graph of f(x) = ax / (x^2 + 1) when A is increased?

The graph compresses vertically

The graph shifts horizontally

The graph stretches vertically

The graph remains unchanged

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does changing B affect the function f(x) = x / (x^2 + B)?

It shifts the graph vertically

It alters the location of critical points

It changes the function's domain

It affects the function's range

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the effect of a negative A on the function's graph?

It shifts the graph upwards

It results in a vertical flip

It results in a horizontal flip

It compresses the graph

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens if B is negative in the function f(x) = ax / (x^2 + B)?

The graph remains unchanged

The graph develops vertical asymptotes

The graph flips horizontally

The function becomes undefined

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