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Chapter 2: Q. 100 (page 116)

Horizontal Shifts Open the horizontal shift applet. Use your mouse to grab the slider and change the value of $h$ . Note the role $h$ plays in the graph of $g (x) = f (x - h)$ , where $f (x) = x^{2}$ .

Short Answer

Expert verified

There is a horizontal shift rightward for $h > 0$ and to the left for $h < 0$

Step by step solution

Given information

Given the function $g (x) = f (x - h)$

Checking the reason

The function $g (x) = f (x - h)$ , it is shifted horizontally right for the values of $h > 0$ and horizontally left for the values of $h < 0$ .

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Most popular questions from this chapter

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$h (x) = \sqrt{x - 2}$

In Problems 7–18, match each graph to one of the following functions:

$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

True or False Every relation is a function.

$f (x) = {(x + 2)}^{3} - 3$

True or False If no domain is specified for a function $f$ , then the domain of $f$ is taken to be the set of real numbers.

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Horizontal Shifts Open the horizontal shift applet. Use your mouse to grab the slider and change the value of h. Note the role hplays in the graph of g(x)=f(x-h), where f(x)=x2.

Short Answer

Step by step solution

Given information

Checking the reason

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Horizontal Shifts Open the horizontal shift applet. Use your mouse to grab the slider and change the value of $h$ . Note the role $h$ plays in the graph of $g (x) = f (x - h)$ , where $f (x) = x^{2}$ .