Share

## Which Statement About The End Behavior Of The Logarithmic Function F(X) = Log(X + 3) – 2 Is True?

Question

Question

### Write The Expression As The Sine, Cosine, Or Tangent Of An Angle. Sin 57° Cos 13° – Cos 57° Sin 13°

### Isiah Determined That 5A2 Is The Gcf Of The Polynomial A3 – 25A2B5 – 35B4. Is He Correct? Explain.

### Which Of The Following Expressions Correctly Determines That X Is Greater Than 10 And Less Than 20?

### A Quantity P Varies Jointly With R And S. Which Expression Represents The Constant Of Variation, K?

### Find The Product Of Z1 And Z2, Where Z1 = 8(Cos 40° + I Sin 40°) And Z2 = 4(Cos 135° + I Sin 135°)

### A Square With An Area Of 4 In² Is Dilated By A Factor Of 7. What Is The Area Of The Dilated Square?

### A Mini Laptop Computer Is On Sale For 40% Off The Regular Price Of $450. How Much Is The Discount?

### Circle O Has A Circumference Of 36Π Cm. What Is The Length Of The Radius, R? 6 Cm 18 Cm 36 Cm 72 Cm

### The Total Fencing Around A Square Field Is 80 Yards. The Field Has An Area Of How Many Square Yards

### If Angle A Has A Measurement Of 42° And Is Complementary To Angle B, What’S The Measure Of Angle B?

### What Is The Equation Of The Line, In Slope-Intercept Form, That Passes Through (4, 2) And (-2, -3)?

### A Quadratic Equation Has Exactly One Real Number Solution. Which Is The Value Of Its Discriminant?

### What Is The Y-Intercept Of The Quadratic Function F(X) = (X – 8)(X + 3)? (8,0) (0,3) (0,–24) (–5,0)

### Osceola County Bonds Worth $1,000 Are Selling At 88.391. What Is The Market Price Of One Such Bond?

### Which Expression Represents The Distance Between The Points (A, 0) And (0, 5) On A Coordinate Grid?

### Find The Product Of Z1 And Z2, Where Z1 = 2(Cos 80° + I Sin 80°) And Z2 = 9(Cos 110° + I Sin 110°)

### An Angle Bisector Of A Triangle Divides The Opposite Side Of The Triangle Into Segments 6Cm And 5Cm

### If 6 Bottles Are Randomly Selected, How Many Ways Are There To Obtain Two Bottles Of Each Variety?

### One Year Ago, You Invested $1,800. Today It Is Worth $1,924.62. What Rate Of Interest Did You Earn?

### The Terminal Side Of An Angle In Standard Position Passes Through P(–3, –4). What Is The Value Of ?

### Eddie Industries Issues $1,500,000 Of 8% Bonds At 105, The Amount Of Cash Received From The Sale Is

### Find The Angle Between The Given Vectors To The Nearest Tenth Of A Degree. U = <-5, 8>, V = <-4, 8>

### What’S The Present Value Of A $900 Annuity Payment Over Five Years If Interest Rates Are 8 Percent?

### If You Know That A Person Is Running 100 Feet Every 12 Seconds, You Can Determine Their __________.

### A Coin Is Tossed 400 Times. Use The Normal Curve Approximation To Find The Probability Of Obtaining

## Answers ( 2 )

## Which Statement About The End Behavior Of The Logarithmic Function F(X) = Log(X + 3) – 2 Is True?

If you are studying the end behavior of the logarithmic function f(x) = log(x + 3) – 2, then you might be wondering which statement about its end behavior is true. Logarithmic functions can be tricky to analyze due to its inverse nature, but understanding it is key for graphing and solving equations. In this article, we will take a closer look at the end behavior of f(x) = log(x + 3) – 2 by examining what happens as x approaches infinity or negative infinity. By the end, you should have a better understanding of how to determine the end behavior of a given logarithmic function.

## The nature of the end behavior of a logarithmic function

When graphed, the logarithmic function f(x) = log(x + ) has asymptotes at x = – and x = . The function approaches these asymptotes as x gets large in either direction.

## The end behavior of the logarithmic function f(x) = log(x + 3) – 2

When x approaches infinity, the logarithmic function f(x) = log(x + 3) – 2 approaches 0. When x approaches negative infinity, the function also approaches 0. This can be seen by taking the limit as x approaches infinity and negative infinity of the logarithmic function f(x) = log(x + 3) – 2.

## Why the end behavior of a logarithmic function is important

The end behavior of the logarithmic function F(X) = Log(X + ) – is important because it describes how the function behaves as X approaches infinity or negative infinity. In particular, the end behavior can be used to determine whether the function is bounded or unbounded.

## How to use the end behavior of a logarithmic function to solve problems

As we know, the end behavior of a logarithmic function is determined by its leading term. In this case, the leading term is . Therefore, the end behavior of is to approach infinity as x approaches infinity, and to approach negative infinity as x approaches 0 from the right.

We can use this information to solve problems involving limits at infinity and horizontal asymptotes. For example, consider the following problem:

Find the limit of as x approaches infinity.

Since the leading term of is , we know that will approach infinity as x approaches infinity. Therefore, we can say that the limit of as x approaches infinity is infinity.

Now let’s look at an example involving a horizontal asymptote. Consider the following function:

The leading term of is , so we know that will approach negative infinity as x approaches 0 from the right. This means that the function has a horizontal asymptote at y = -∞.

## Conclusion

In conclusion, the end behavior of the logarithmic function f(x) = log(x + 3) – 2 is positive infinity when x approaches negative infinity and negative infinity when x approaches positive infinity. This is due to the fact that as x increases, the value inside the brackets (x + 3) becomes larger and larger, thus resulting in a higher logarithm result which tends toward positive or negative infinity depending on its sign. As such, it can be concluded that this type of function has an infinite range at both ends of its domain.

Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) – 2 is true?

Understanding the end behavior of a logarithmic function can be a bit tricky, but it’s important to know in order to accurately utilize the function in problem-solving. So, let’s dive into the statement and break it down!

The end behavior of a logarithmic function is determined by the sign of the base and the sign of the exponent. In the case of the statement in question, the base is x + 3 and the exponent is -2. Since the base is positive, the end behavior of the function is determined by the sign of the exponent.

Since the exponent is negative, the function decreases without bound as the input increases. This means that the end behavior of the function f(x) = log(x + 3) – 2 is that it decreases without bound as the input increases.

So, there you have it! The statement that is true about the end behavior of the logarithmic function f(x) = log(x + 3) – 2 is that it decreases without bound as the input increases.

It’s always important to understand the end behavior of a function before utilizing it in problem-solving. Now that you understand the end behavior of this particular logarithmic function, you can use it with confidence!