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Exponential Decay Function Concepts

Exponential Decay Function Concepts

Assessment

Interactive Video

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

Created by

Patricia Brown

FREE Resource

The video tutorial explains the parent exponential function f(x) = a^x, where a is positive and not equal to 1. It covers the domain and range of exponential functions, highlighting that the domain is all real numbers and the range is positive values excluding zero. The tutorial distinguishes between exponential growth and decay, explaining that growth occurs when a > 1, and decay when a is a fraction between 0 and 1. Key characteristics such as intercepts, continuity, and the behavior of the function as x increases are discussed for both growth and decay scenarios.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the domain of the parent exponential function f(x) = a^x?

All negative numbers

All positive numbers

All real numbers

Only integers

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is true about the range of the parent exponential function?

It is limited to positive integers

It includes negative numbers

It starts from zero but does not include it

It includes zero

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the y-intercept of the parent exponential function?

(1, 0)

(0, 0)

(1, 1)

(0, 1)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why does the parent exponential function not have an x-intercept?

Because it has a horizontal asymptote at y = 0

Because it is a linear function

Because it is a decreasing function

Because it is not defined for x = 0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the function f(x) = a^x as x increases?

It decreases

It remains constant

It increases

It oscillates

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the base condition for the function f(x) = a^(-x) to indicate exponential decay?

a < 1

a = 1

a > 1

a = 0

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the base of the function f(x) = a^(-x) be transformed to indicate decay?

By making it a fraction between 0 and 1

By making it a negative number

By making it greater than 1

By making it equal to 1

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