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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

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 The domain of the function $f (x) = \frac{x^{2} - 4}{x}$ is ${x | x \neq \pm 2}$ .

Write the point–slope form of the line with slope 5 containing the point (3, -2).

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

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.

$h (x) = \frac{1}{2 x}$

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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 $y = g (x) = f (x) + k$