Type The Correct Answer In Each Box. Round Your Answers To One Decimal Place. Use The Function G ( X ) = 4 ( 0.6 ) X G(x) = 4(0.6)^x G ( X ) = 4 ( 0.6 ) X To Complete The Table And Find The Y Y Y -intercept.

Introduction

In this article, we will explore the concept of the y-intercept of a function and how to find it using a given function. The y-intercept is a point on the graph of a function where the x-coordinate is zero. It is an important concept in mathematics, particularly in algebra and calculus.

The Function

The function we will be using is $g(x) = 4(0.6)^x$. This is an exponential function, which means that the output value is a constant raised to the power of the input value. In this case, the constant is 4 and the base is 0.6.

The Table

To find the y-intercept, we need to complete the table with the values of x and the corresponding values of g(x). We will use the function $g(x) = 4(0.6)^x$ to calculate the values of g(x) for different values of x.

x	g(x)
0
1
2
3
4

Calculating the Values of g(x)

To calculate the values of g(x), we will substitute the values of x into the function $g(x) = 4(0.6)^x$.

For x = 0: $g(0) = 4(0.6)^0 = 4(1) = 4$

For x = 1: $g(1) = 4(0.6)^1 = 4(0.6) = 2.4$

For x = 2: $g(2) = 4(0.6)^2 = 4(0.36) = 1.44$

For x = 3: $g(3) = 4(0.6)^3 = 4(0.216) = 0.864$

For x = 4: $g(4) = 4(0.6)^4 = 4(0.1296) = 0.5184$

Completing the Table

Now that we have calculated the values of g(x) for different values of x, we can complete the table.

x	g(x)
0	4.0
1	2.4
2	1.4
3	0.9
4	0.5

Finding the y-Intercept

The y-intercept is the point on the graph of a function where the x-coordinate is zero. In this case, the x-coordinate is 0, so we need to find the value of g(x) when x = 0.

From the table, we can see that when x = 0, g(x) = 4.0. Therefore, the y-intercept of the function $g(x) = 4(0.6)^x$ is (0, 4.0).

Conclusion

In this article, we have explored the concept of the y-intercept of a function and how to find it using a given function. We have used the function $g(x) = 4(0.6)^x$ to complete the table and find the y-intercept. The y-intercept is an important concept in mathematics, particularly in algebra and calculus.

Key Takeaways

• The y-intercept is a point on the graph of a function where the x-coordinate is zero.
• To find the y-intercept, we need to substitute x = 0 into the function.
• The y-intercept of the function $g(x) = 4(0.6)^x$ is (0, 4.0).

Further Reading

If you want to learn more about the y-intercept and how to find it using different functions, you can check out the following resources:

• Khan Academy: Y-Intercept
• Mathway: Y-Intercept
• Wolfram Alpha: Y-Intercept

Practice Problems

If you want to practice finding the y-intercept of different functions, you can try the following problems:

• Find the y-intercept of the function $f(x) = 2(0.8)^x$.
• Find the y-intercept of the function $h(x) = 3(0.9)^x$.

Answer Key

x	g(x)
0	4.0
1	2.4
2	1.4
3	0.9
4	0.5

Introduction

In our previous article, we explored the concept of the y-intercept of a function and how to find it using a given function. In this article, we will answer some frequently asked questions about finding the y-intercept of a function.

Q: What is the y-intercept of a function?

A: The y-intercept of a function is a point on the graph of a function where the x-coordinate is zero. It is the value of the function when the input is zero.

Q: How do I find the y-intercept of a function?

A: To find the y-intercept of a function, you need to substitute x = 0 into the function. This will give you the value of the function when the input is zero.

Q: What if the function is not in the form f(x) = a(x - h)^2 + k?

A: If the function is not in the form f(x) = a(x - h)^2 + k, you can still find the y-intercept by substituting x = 0 into the function. However, you may need to use algebraic manipulations to simplify the function before substituting x = 0.

Q: Can I use a graphing calculator to find the y-intercept of a function?

A: Yes, you can use a graphing calculator to find the y-intercept of a function. Simply enter the function into the calculator and use the "zero" or "intercept" feature to find the y-intercept.

Q: What if the function has a negative exponent?

A: If the function has a negative exponent, you can still find the y-intercept by substituting x = 0 into the function. However, you may need to use algebraic manipulations to simplify the function before substituting x = 0.

Q: Can I find the y-intercept of a function with a variable in the exponent?

A: Yes, you can find the y-intercept of a function with a variable in the exponent. However, you may need to use algebraic manipulations to simplify the function before substituting x = 0.

Q: What if the function is a rational function?

A: If the function is a rational function, you can still find the y-intercept by substituting x = 0 into the function. However, you may need to use algebraic manipulations to simplify the function before substituting x = 0.

Q: Can I use a computer algebra system (CAS) to find the y-intercept of a function?

A: Yes, you can use a computer algebra system (CAS) to find the y-intercept of a function. Simply enter the function into the CAS and use the "solve" or "intercept" feature to find the y-intercept.

Conclusion

In this article, we have answered some frequently asked questions about finding the y-intercept of a function. We have covered topics such as how to find the y-intercept, what to do if the function is not in the form f(x) = a(x - h)^2 + k, and how to use a graphing calculator or computer algebra system (CAS) to find the y-intercept.

Key Takeaways

• The y-intercept of a function is a point on the graph of a function where the x-coordinate is zero.
• To find the y-intercept, you need to substitute x = 0 into the function.
• You can use a graphing calculator or computer algebra system (CAS) to find the y-intercept of a function.

Further Reading

If you want to learn more about finding the y-intercept of a function, you can check out the following resources:

• Khan Academy: Y-Intercept
• Mathway: Y-Intercept
• Wolfram Alpha: Y-Intercept

Practice Problems

If you want to practice finding the y-intercept of different functions, you can try the following problems:

• Find the y-intercept of the function f(x) = 2(x - 1)^2 + 3.
• Find the y-intercept of the function g(x) = 3(x + 2)^2 - 4.
• Find the y-intercept of the function h(x) = 4(x - 3)^2 + 2.

Answer Key

x	g(x)
0	4.0
1	2.4
2	1.4
3	0.9
4	0.5

Note: The answer key is the same as the table above.