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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 97 (page 116)

Explain how the range of a function $y = f (x) = x^{2}$ compares to $y = g (x) = f (x) + k$

Short Answer

Expert verified

The graph shifts vertically upward $k$ units when $k > 0$ and $k < 0$ vertically downwards $k$ units

Step by step solution

Given information

Given the equation $y = x^{2}$ and

$y = f (x) + k$

Checking the effect of k

Here if $k > 0$ the graph shifts by $k$ units vertically upward and $k$ units vertically downward by $k$ units for $k < 0$

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Most popular questions from this chapter

True or False

To obtain the graph of $f (x) = x^{3} + 5,$ shift the graph of $y = x^{3}$ vertically up $5$ units.

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

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

If $f (x) = \{\begin{cases} 2 x - 4 i f - 1 鈮� x 鈮� 2 \\ x^{3} - 2 i f 2 < x 鈮� 3 \end{cases}$

Find: (a) $f (0)$ (b) $f (1)$ (c) $f (2)$ (d) $f (3)$

If $f (x) = \{\begin{cases} x^{3} i f - 2 鈮� x < 1 \\ 3 x + 2 i f 1 鈮� x 鈮� 4 \end{cases}$

Find: (a) $f (- 1)$ (b) $f (0)$ (c) $f (1)$ (d) $f (3)$

If $(4, 2)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = f 2 (x)$ ?

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91影视

Explain how the range of a function y=f(x)=x2 compares toy=g(x)=f(x)+k

Short Answer

Step by step solution

Given information

Checking the effect of k

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Explain how the range of a function $y = f (x) = x^{2}$ compares to $y = g (x) = f (x) + k$