Write The Equation For The Function \[$ G(x) \$\], Which Can Be Described As A Vertical Shift \[$ 1 \frac{1}{2} \$\] Units Up From The Function \[$ F(x) = \ln X - 1 \$\].

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Vertical Shifts in Functions: Understanding the Equation for g(x)

In mathematics, functions are used to describe relationships between variables. A vertical shift in a function is a transformation that moves the graph of the function up or down by a certain number of units. In this article, we will discuss how to write the equation for a function g(x), which is a vertical shift of 1 1/2 units up from the function f(x) = ln x - 1.

A vertical shift in a function is a transformation that moves the graph of the function up or down by a certain number of units. This type of transformation does not change the shape or size of the graph, but only its position. In the case of a vertical shift up, the graph is moved up by the specified number of units, while in the case of a vertical shift down, the graph is moved down by the specified number of units.

The Function f(x) = ln x - 1

The function f(x) = ln x - 1 is a logarithmic function that has a base of e (approximately 2.718). The natural logarithm of a number is the power to which e must be raised to produce that number. In this case, the function f(x) = ln x - 1 is a horizontal shift of the natural logarithm function down by 1 unit.

The Vertical Shift of 1 1/2 Units Up

To write the equation for the function g(x), which is a vertical shift of 1 1/2 units up from the function f(x) = ln x - 1, we need to add 1 1/2 to the function f(x) = ln x - 1. This will move the graph of the function f(x) = ln x - 1 up by 1 1/2 units.

To write the equation for g(x), we need to add 1 1/2 to the function f(x) = ln x - 1. This can be done by adding 1 1/2 to the function f(x) = ln x - 1, which gives us:

g(x) = ln x - 1 + 1 1/2

To simplify this equation, we can convert the mixed number 1 1/2 to an improper fraction, which is 3/2. We can then add this to the function f(x) = ln x - 1, which gives us:

g(x) = ln x - 1 + 3/2

To simplify this equation further, we can combine the terms on the right-hand side, which gives us:

g(x) = ln x + 1/2 - 1

We can then simplify this equation further by combining the constants on the right-hand side, which gives us:

g(x) = ln x - 1/2

In this article, we discussed how to write the equation for a function g(x), which is a vertical shift of 1 1/2 units up from the function f(x) = ln x - 1. We saw that a vertical shift in a function is a transformation that moves the graph of the function up or down by a certain number of units. We also saw that to write the equation for g(x), we need to add 1 1/2 to the function f(x) = ln x - 1. This can be done by adding 1 1/2 to the function f(x) = ln x - 1, which gives us g(x) = ln x - 1 + 3/2. We can then simplify this equation further by combining the terms on the right-hand side, which gives us g(x) = ln x + 1/2 - 1. Finally, we can simplify this equation further by combining the constants on the right-hand side, which gives us g(x) = ln x - 1/2.

  1. Write the equation for the function g(x), which is a vertical shift of 2 units up from the function f(x) = 2x - 3.
  2. Write the equation for the function g(x), which is a vertical shift of 1/2 unit down from the function f(x) = x^2 + 2.
  3. Write the equation for the function g(x), which is a vertical shift of 3 units down from the function f(x) = 2x^2 - 1.
  1. To write the equation for the function g(x), which is a vertical shift of 2 units up from the function f(x) = 2x - 3, we need to add 2 to the function f(x) = 2x - 3. This gives us:

g(x) = 2x - 3 + 2

We can then simplify this equation by combining the constants on the right-hand side, which gives us:

g(x) = 2x - 1

  1. To write the equation for the function g(x), which is a vertical shift of 1/2 unit down from the function f(x) = x^2 + 2, we need to subtract 1/2 from the function f(x) = x^2 + 2. This gives us:

g(x) = x^2 + 2 - 1/2

We can then simplify this equation by combining the constants on the right-hand side, which gives us:

g(x) = x^2 + 3/2

  1. To write the equation for the function g(x), which is a vertical shift of 3 units down from the function f(x) = 2x^2 - 1, we need to subtract 3 from the function f(x) = 2x^2 - 1. This gives us:

g(x) = 2x^2 - 1 - 3

We can then simplify this equation by combining the constants on the right-hand side, which gives us:

g(x) = 2x^2 - 4
Vertical Shifts in Functions: A Q&A Guide

In our previous article, we discussed how to write the equation for a function g(x), which is a vertical shift of 1 1/2 units up from the function f(x) = ln x - 1. In this article, we will answer some frequently asked questions about vertical shifts in functions.

Q: What is a vertical shift in a function?

A: A vertical shift in a function is a transformation that moves the graph of the function up or down by a certain number of units. This type of transformation does not change the shape or size of the graph, but only its position.

Q: How do I write the equation for a function g(x), which is a vertical shift of a certain number of units up or down from the function f(x)?

A: To write the equation for a function g(x), which is a vertical shift of a certain number of units up or down from the function f(x), you need to add or subtract the specified number of units from the function f(x).

Q: What is the difference between a vertical shift up and a vertical shift down?

A: A vertical shift up moves the graph of the function up by the specified number of units, while a vertical shift down moves the graph of the function down by the specified number of units.

Q: Can I have a negative vertical shift?

A: Yes, you can have a negative vertical shift. A negative vertical shift means that the graph of the function will be moved down by the specified number of units.

Q: How do I determine the equation for a function g(x), which is a vertical shift of a certain number of units up or down from the function f(x)?

A: To determine the equation for a function g(x), which is a vertical shift of a certain number of units up or down from the function f(x), you need to add or subtract the specified number of units from the function f(x).

Q: Can I have a vertical shift of a fraction of a unit?

A: Yes, you can have a vertical shift of a fraction of a unit. A fraction of a unit is a decimal or a fraction that represents a part of a unit.

Q: How do I write the equation for a function g(x), which is a vertical shift of a fraction of a unit up or down from the function f(x)?

A: To write the equation for a function g(x), which is a vertical shift of a fraction of a unit up or down from the function f(x), you need to add or subtract the specified fraction of a unit from the function f(x).

Q: Can I have a vertical shift of a negative fraction of a unit?

A: Yes, you can have a vertical shift of a negative fraction of a unit. A negative fraction of a unit means that the graph of the function will be moved down by the specified fraction of a unit.

Q: How do I determine the equation for a function g(x), which is a vertical shift of a negative fraction of a unit up or down from the function f(x)?

A: To determine the equation for a function g(x), which is a vertical shift of a negative fraction of a unit up or down from the function f(x), you need to subtract the specified negative fraction of a unit from the function f(x).

In this article, we answered some frequently asked questions about vertical shifts in functions. We discussed how to write the equation for a function g(x), which is a vertical shift of a certain number of units up or down from the function f(x). We also discussed how to determine the equation for a function g(x), which is a vertical shift of a fraction of a unit up or down from the function f(x). We hope that this article has been helpful in understanding vertical shifts in functions.

  1. Write the equation for the function g(x), which is a vertical shift of 2 units up from the function f(x) = 2x - 3.
  2. Write the equation for the function g(x), which is a vertical shift of 1/2 unit down from the function f(x) = x^2 + 2.
  3. Write the equation for the function g(x), which is a vertical shift of 3 units down from the function f(x) = 2x^2 - 1.
  1. To write the equation for the function g(x), which is a vertical shift of 2 units up from the function f(x) = 2x - 3, we need to add 2 to the function f(x) = 2x - 3. This gives us:

g(x) = 2x - 3 + 2

We can then simplify this equation by combining the constants on the right-hand side, which gives us:

g(x) = 2x - 1

  1. To write the equation for the function g(x), which is a vertical shift of 1/2 unit down from the function f(x) = x^2 + 2, we need to subtract 1/2 from the function f(x) = x^2 + 2. This gives us:

g(x) = x^2 + 2 - 1/2

We can then simplify this equation by combining the constants on the right-hand side, which gives us:

g(x) = x^2 + 3/2

  1. To write the equation for the function g(x), which is a vertical shift of 3 units down from the function f(x) = 2x^2 - 1, we need to subtract 3 from the function f(x) = 2x^2 - 1. This gives us:

g(x) = 2x^2 - 1 - 3

We can then simplify this equation by combining the constants on the right-hand side, which gives us:

g(x) = 2x^2 - 4