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Chapter 1: Problem 130

What must be done to a function's equation so that its graph is shifted horizontally to the right?

Short Answer

Expert verified
To shift the graph of a function to the right, add a positive value inside the parentheses with the variable in the function's equation, e.g., \( f(x-h) \).

Step by step solution

01

Understand the effect of horizontal shifts

A horizontal shift, also known as a horizontal translation, moves the function's graph left or right. It doesn't change the shape or orientation of the graph. An increase in the input (x-value) corresponds to a shift to the right, while a decrease corresponds to a shift to the left.
02

Identify the key part in function's equation responsible for horizontal shift

Horizontal shifts are implemented in the function's equation by adding or subtracting a value 'h' inside the parentheses with the variable, like this: \( f(x-h) \). If 'h' is positive, the graph shifts to the right. If 'h' is negative, the graph shifts to the left.
03

Specify the condition for shifting the function's graph to the right

To shift the function's graph to the right, add a positive constant 'h' inside the parentheses with the variable in the function's equation. The new function will look like this: \( f(x-h) \).

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. -Consider the function defined by $$\\{(-2,4),(-1,1),(1,1),(2,4)\\}$$ Reverse the components of each ordered pair and write the eresulting relation. Is this relation a function?

Will help you prepare for the material covered in the next section. Write an algebraic expression for the fare increase if a 200 dollars plane ticket is increased to \(x\) dollars.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph of \((x-2)^{2}+(y+1)^{2}=16\) is my graph of \(x^{2}+y^{2}=16\) translated two units right and one unit down.

Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$x^{2}+y^{2}=25$$

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}(x-2)^{2}+(y+3)^{2} &=4 \\\y &=x-3\end{aligned}$$
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