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Chapter 1: Q25E (page 22)

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\({\bf{y = - }}\sqrt({\bf{3}}){{\bf{x}}}\)

Short Answer

Expert verified

The graph is shown below.

Step by step solution

01

Given data

We are given the transformed graph \(y = - \sqrt(3){x}\)

02

Solution\(\)\(\) \(\)

We can see that the basic graph must be \(y = f\left( x \right) = \sqrt(3){x}\) seen in red below.

This is in our tool box of “standard function” called the cube root function.

The functional connection between the transformed graph and the basic graph is given by \(y = - f\left( x \right)\).

03

The graph is shown below:

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Most popular questions from this chapter

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function\({\bf{f = }}\frac{{\bf{9}}}{{\bf{5}}}{\bf{c + 32}}{\bf{.}}\)

(a) Sketch a graph of this function

(b)What is the slope of the graph and what does it represent? What is the

F-intercept and what does it represent?

Use the table to evaluate each expression.

(a) \(f\left( {g\left( 2 \right)} \right)\) (b) \(g\left( {f\left( 0 \right)} \right)\) (c) \(f \circ g\left( 0 \right)\) (d) \(g \circ f\left( 6 \right)\) (e) \(g \circ g\left( { - 2} \right)\) (f) \(f \circ f\left( 4 \right)\)

Explain how each graph is obtained from the graph of\({\bf{y = f}}\left( {\bf{x}} \right)\).

(a)\({\bf{y = f}}\left( {\bf{x}} \right){\bf{ + 8}}\)

(b)\({\bf{y = f}}\left( {{\bf{x + 8}}} \right)\)\(\begin{array}{l}{\bf{y = f}}\left( {{\bf{x + 8}}} \right)\\{\bf{y = 8f}}\left( {\bf{x}} \right)\\{\bf{y = f}}\left( {{\bf{8x}}} \right)\\{\bf{y = - f}}\left( {\bf{x}} \right){\bf{ - 1}}\\{\bf{y = 8f}}\left( {\frac{{\bf{1}}}{{\bf{8}}}{\bf{x}}} \right)\\\end{array}\)

(c)\({\bf{y = 8f}}\left( {\bf{x}} \right)\)

(d)\({\bf{y = f}}\left( {{\bf{8x}}} \right)\)\(\)

(e)\({\bf{y = - f}}\left( {\bf{x}} \right){\bf{ - 1}}\)

(f)\({\bf{y = 8f}}\left( {\frac{{\bf{1}}}{{\bf{8}}}{\bf{x}}} \right)\)

Prove the statement using the\(\varepsilon \), \(\delta \)definition of a limit.

\(\mathop {\lim }\limits_{x \to a} x = a\)

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\(y = \frac{1}{4}tan\left( {x - \frac{\pi }{4}} \right)\)
See all solutions

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