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Chapter 2: Problem 129

What must be done to a function's equation so that its graph is shifted vertically upward?

Short Answer

Expert verified
To shift the graph of a function vertically upward, a positive constant needs to be added to the function's equation.

Step by step solution

01

Understanding Vertical Transformations

When a constant is added (or subtracted) to a function, it causes a shift in the graph of the function along the y-axis. This is known as vertical transformation. The magnitude and direction of the shift is determined by the value and sign of the constant.
02

Application to the Function's Equation

To shift a function's graph upwards, a positive constant must be added to the function. Specifically, if \( f(x) \) is the original function, the transformed function \( g(x) \) would be \( g(x) = f(x) + c \), where \( c \) is a positive constant. The value of \( c \) determines how much the function's graph is shifted upward.

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Most popular questions from this chapter

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\sqrt[3]{2-x} $$

If you are given a function's equation, how do you determine if the function is even, odd, or neither?

Begin by graphing the cube root function, \(f(x)-\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$ g(x)-\sqrt[3]{x+2} $$

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=(x-1)^{3} $$

Explain how to determine if two functions are inverses of each other.
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