4th Edition

ISBN: 9780135874738

Author: Sullivan

Publisher: PEARSON

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The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

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Textbook Question

Chapter 1.1, Problem 115AYU

Are the functions $f (x) = x - 1$ and $g (x) = \frac{x^{2} - 1}{x + 1}$ the same? Explain.

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Chapter 1.1, Problem 114AYU

Chapter 1.1, Problem 117AYU

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A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

The graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is given above. (A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter "DNE". If a limit can be represented by -∞o or ∞o, then do so. lim f(z) +3 lim f(z) 1-1 lim f(z) f(1) = 2 = -4 = undefined lim f(z) 1 2-1 lim f(z): 2-1+ lim f(x) 2+1 -00 = -2 = DNE f(-1) = -2 lim f(z) = -2 1-4 lim f(z) 2-4° 00 f'(0) f'(2) = = (B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left- continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If there are none, enter "none". Discontinuous at z = Left-continuous at x = Invalid use of a comma.syntax incomplete. Right-continuous at z = Invalid use of a comma.syntax incomplete. (C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5).…

A graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

Chapter 1 Solutions

PRECALCULUS:CONCEPTS...-MYLAB+ETEXT

Ch. 1.1 - The inequality 1x3 can be written in interval...Ch. 1.1 - 2. If , the value of the expression is _______ ...Ch. 1.1 - 3. The domain of the variable in the expression is...Ch. 1.1 - 4. Solve the inequality: . Graph the solution set....Ch. 1.1 - To rationalize the denominator of 3 5 2 , multiply...Ch. 1.1 - 6. A quotient is considered rationalized if its...Ch. 1.1 - If f is a function defined by the equation y=f(x),...Ch. 1.1 - If f(x)=x+1 and g(x)=x3, then ____________x3(x+1).Ch. 1.1 - True or False Every relation is a function.Ch. 1.1 - True or False The domain (f.g)(x) consists of the...

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Are the functions f ( x ) = x − 1 and g ( x ) = x 2 − 1 x + 1 the same? Explain.

Solution Summary: The author explains that the functions f (x) = x 1 and g ( X ), are not equivalent. They are different functions.

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