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Chapter 1: Problem 52

Write an equation for the function described by the given characteristics. The shape of \(f(x)=|x|\), but shifted four units to the left and eight units down

Short Answer

Expert verified
The function with the mentioned transformation is \(f(x) = |x+4| -8\).

Step by step solution

01

Recognize the Base Function

The base function given is \(f(x) = |x|\). This is an absolute value function.
02

Account for the Horizontal Shift

The function will be shifted four units to the left. This can be represented in the function by replacing \(x\) with \(x+4\) in the base function. So our function becomes \(f(x) = |x+4|\).
03

Account for the Vertical Shift

The function will be shifted eight units down. This can be done by subtracting 8 from the function. So our function, with both shifts accounted becomes \(f(x) = |x+4| -8\).

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Most popular questions from this chapter

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=(x-1)^{3}+2$$

Given $$f(x)=x^{2}$$ is \(f\) the independent variable? Why or why not?

Sketch the graph of the function. $$g(x)=[[x]]-1$$

Determine whether the statements use the word function in ways that are mathematically correct. Explain your reasoning. (a) The amount in your savings account is a function of your salary. (b) The speed at which a free-falling baseball strikes the ground is a function of the height from which it was dropped.

Determine whether the statement is true or false. Justify your answer. The set of ordered pairs \(\\{(-8,-2),(-6,0),(-4,0)\) \((-2,2),(0,4),(2,-2)\\}\) represents a function.
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