/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 78 The graph of \(y=f(x)\) passes t... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 78

The graph of \(y=f(x)\) passes through the points \((0,1),(1,2),\) and \((2,3) .\) Find the corresponding points on the graph of \(y=f(x+2)-1\).

Short Answer

Expert verified
The corresponding points on the graph of \(f(x+2) - 1\) will be \((-2, 0), (-1, 1), (0, 2)\).

Step by step solution

01

Shifting the x-coordinate

This step involves moving the x-coordinates to left by 2 units. Hence, if a point on \(f(x)\) is \((a, b)\), its corresponding point on the graph of \(f(x+2) - 1\) will have x-coordinate \(a - 2\). So the points \((0, 1), (1, 2), (2, 3)\) on \(f(x)\) will be transformed to \((-2, 1), (-1, 2), (0, 3)\) respectively on \(f(x+2) - 1\).
02

Shifting the y-coordinate

The final step is to shift these new points down by 1 unit. So, if a point on the graph of \(f(x+2)\) is \((a, b)\), then its corresponding point on \(f(x+2)-1\) will have y-coordinate \(b - 1\). Thus, \((-2, 1), (-1, 2), (0, 3)\) will be shifted down to \((-2, 0), (-1, 1), (0, 2)\) respectively.

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Most popular questions from this chapter

Your wage is \(\$ 12.00\) per hour plus \(\$ 0.55\) for each unit produced per hour. So, your hourly wage \(y\) in terms of the number of units produced \(x\) is \(y=12+0.55 x.\) (a) Find the inverse function. What does each variable in the inverse function represent? (b) Use a graphing utility to graph the function and its inverse function. (c) Use the trace feature of the graphing utility to find the hourly wage when 9 units are produced per hour. (d) Use the trace feature of the graphing utility to find the number of units produced per hour when your hourly wage is \(\$ 21.35\)

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Prove that a function of the following form is odd. $$y=a_{2 n+1} x^{2 n+1}+a_{2 n-1} x^{2 n-1}+\cdots+a_{3} x^{3}+a_{1} x$$

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