Limits at Infinity of Algebraic Functions Quiz

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What can be said about the limit at negative infinity of logarithmic functions?

It exists and is equal to 0

It exists and is equal to a specific constant value

It does not exist (correct)

It exists and is equal to infinity

For polynomial functions with a leading coefficient 'a' that is greater than 0 and an odd degree 'n', what is the limit at positive infinity?

Zero

Negative infinity

Positive infinity (correct)

A specific constant value

When finding the limit at infinity of rational functions, what is the case if the degrees of the numerator and denominator are equal?

The limit exists and is a specific constant value (correct)

The limit is always infinity

The limit is always 0

The limit does not exist

What can be concluded about the limit at infinity of exponential functions with a base 'b' greater than 1?

It is always infinity Signup and view all the answers

In the context of polynomial functions, what happens to the limit at negative infinity if 'a' is negative and 'n' is even?

It is negative infinity Signup and view all the answers

When dealing with rational functions, what can be said about the limit if 'n' is greater than 'm' and 'a = b'?

It exists and is equal to infinity Signup and view all the answers

For a polynomial function of degree n and leading coefficient a, what happens to the limits at infinity if a is less than 0 and n is even?

The limit approaches negative infinity. Signup and view all the answers

In which scenario do rational functions differ from polynomial functions in terms of end behaviors?

When the function has multiple branches. Signup and view all the answers

If n is odd in a polynomial function, how are the right and left ends of the graph positioned?

In opposite directions. Signup and view all the answers

What happens to the limits at infinity of a rational function if the function has one branch?

The limit approaches zero. Signup and view all the answers

In a rational function with one branch, what can be said about its end behavior compared to polynomial functions?

They have different end behaviors. Signup and view all the answers

What is the end behavior of a rational function with one branch if it approaches zero at infinity?

It approaches zero. Signup and view all the answers

As 𝑥 approaches positive or negative infinity, what happens to 𝑦 in relation to the 𝑥-axis?

𝑦 becomes closer to the 𝑥-axis but will never intersect it. Signup and view all the answers

What is the horizontal asymptote of the function 𝑓(𝑥) as defined in the text?

𝑓(𝑥) = 0 Signup and view all the answers

What is the limit as 𝑥 approaches positive or negative infinity of 𝑥^5?

∞ Signup and view all the answers

What is the general first step to evaluate limits at infinity of rational functions?

Divide first the numerator and denominator by the largest power of 𝑥 in the denominator. Signup and view all the answers

What is the limit as 𝑥 approaches ±∞ of a rational function where the denominator has a higher degree than the numerator?

0 Signup and view all the answers

What should be done to prevent bad bacteria from multiplying each day in a human body?

Maintain a healthy diet and lifestyle Signup and view all the answers

What value does the limit of a function approach as 𝑥 increases without bound?

Infinity Signup and view all the answers

In evaluating the limit of algebraic functions, what are the end behaviors of polynomial functions dependent on?

The degree of the polynomial Signup and view all the answers

How can one compute the limits of exponential, logarithmic, and trigonometric functions?

Using tables of values and graphs of the functions Signup and view all the answers

What do limits at infinity of some algebraic and transcendental functions help illustrate?

The end behavior of functions as 𝑥 tends to infinity/decreases to negative infinity Signup and view all the answers

What is key in computing the limits at infinity of algebraic and transcendental functions?

Understanding the behavior of the function as 𝑥 approaches infinity Signup and view all the answers

What is the limit of $e^x$ as $x$ approaches $- ext{infinity}$?

$0$ Signup and view all the answers

What is the limit of $\log_b(x)$ as $x$ approaches $\infty$, where $b > 1$?

$\infty$ Signup and view all the answers

For polynomial functions of even degrees and an odd degree, what are the leading coefficients assumed to be when approaching $- ext{infinity}$?

Positive Signup and view all the answers

What is the limit of $\ln(x)$ as $x$ approaches $\infty$?

$\infty$ Signup and view all the answers

What happens to the limit of $\log_{b}(x)$ as $x$ approaches $-\infty$, where $0 < b < 1$?

Does not exist Signup and view all the answers

In the context of limits at infinity, what happens to the limit of exponential functions as the exponent increases towards infinity?

$\infty$ Signup and view all the answers

Limits at Infinity of Algebraic Functions Quiz

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Questions and Answers

What can be said about the limit at negative infinity of logarithmic functions?

For polynomial functions with a leading coefficient 'a' that is greater than 0 and an odd degree 'n', what is the limit at positive infinity?

When finding the limit at infinity of rational functions, what is the case if the degrees of the numerator and denominator are equal?

What can be concluded about the limit at infinity of exponential functions with a base 'b' greater than 1?

In the context of polynomial functions, what happens to the limit at negative infinity if 'a' is negative and 'n' is even?

When dealing with rational functions, what can be said about the limit if 'n' is greater than 'm' and 'a = b'?

For a polynomial function of degree n and leading coefficient a, what happens to the limits at infinity if a is less than 0 and n is even?

In which scenario do rational functions differ from polynomial functions in terms of end behaviors?

If n is odd in a polynomial function, how are the right and left ends of the graph positioned?

What happens to the limits at infinity of a rational function if the function has one branch?

In a rational function with one branch, what can be said about its end behavior compared to polynomial functions?

What is the end behavior of a rational function with one branch if it approaches zero at infinity?

As 𝑥 approaches positive or negative infinity, what happens to 𝑦 in relation to the 𝑥-axis?

What is the horizontal asymptote of the function 𝑓(𝑥) as defined in the text?

What is the limit as 𝑥 approaches positive or negative infinity of 𝑥^5?

What is the general first step to evaluate limits at infinity of rational functions?

What is the limit as 𝑥 approaches ±∞ of a rational function where the denominator has a higher degree than the numerator?

What should be done to prevent bad bacteria from multiplying each day in a human body?

What value does the limit of a function approach as 𝑥 increases without bound?

In evaluating the limit of algebraic functions, what are the end behaviors of polynomial functions dependent on?

How can one compute the limits of exponential, logarithmic, and trigonometric functions?

What do limits at infinity of some algebraic and transcendental functions help illustrate?

What is key in computing the limits at infinity of algebraic and transcendental functions?

What is the limit of $e^x$ as $x$ approaches $- ext{infinity}$?

What is the limit of $\log_b(x)$ as $x$ approaches $\infty$, where $b > 1$?

For polynomial functions of even degrees and an odd degree, what are the leading coefficients assumed to be when approaching $- ext{infinity}$?

What is the limit of $\ln(x)$ as $x$ approaches $\infty$?

What happens to the limit of $\log_{b}(x)$ as $x$ approaches $-\infty$, where $0 < b < 1$?

In the context of limits at infinity, what happens to the limit of exponential functions as the exponent increases towards infinity?

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