Explanation Translation and reflection of function: Let f be any function and let h and k be any positive constants. 1. The graph of y = f ( x ) + k is the graph of y = f ( x ) translated upward k units. 2. The graph of y = f ( x ) − k is the graph of y = f ( x ) translated downward by k units. 3. The graph of y = f ( x − h ) is the graph of y = f ( x ) translated to the right by h units. 4. The graph of y = f ( x + h ) is the graph of y = f ( x ) translated to the left by h units. 5. The graph of y = − f ( x ) is the graph of y = f ( x ) reflected vertically across the x- axis, that is turned upside down. 6. The graph of y = f ( − x ) is the graph of y = f ( x ) reflected horizontally across the y- axis, that is mirror image. Description: The graph of the function f ( x ) = e x is shown below using the graphical calculator. Find the location of the graphs of f ( x ) = e x − 4 from the graph f ( x ) = e x . The given function is exponential function. The functions are f ( x ) = e x − 4 and f ( x ) = e x . Apply the concept 3 mentioned above for the given statement. Form the function f ( x ) = e x − 4 , it can be written as f ( x ) = e x and h = 4 . That is, the graph of f ( x ) = e x − 4 resembles to the graph of f ( x ) = e x translated to right by 4 units. Find the location of the graphs of f ( x ) = e x − 6 from the graph f ( x ) = e x

10th Edition

ISBN: 9781285195728

Author: Jerome E. Kaufmann, Karen L. Schwitters

Publisher: Cengage Learning

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 11.2, Problem 50PS

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The function f(x)=ex and find the location of the graphs of f(x)=ex−4, f(x)=ex−6, and f(x)=ex+5. Graph all three functions on the same set of axes with f(x)=ex.

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Chapter 11.2, Problem 49PS

Chapter 11.2, Problem 51PS

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R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

Question 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]

part b please

Chapter 11 Solutions

Intermediate Algebra

Ch. 11.1 - For Problems 1-10 answer true or false If 2x+1=23x...Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 3CQ Ch. 11.1 - Prob. 4CQ Ch. 11.1 - Prob. 5CQ Ch. 11.1 - Prob. 6CQ Ch. 11.1 - Prob. 7CQ Ch. 11.1 - Prob. 8CQ Ch. 11.1 - Prob. 9CQ Ch. 11.1 - Prob. 10CQ

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To graph: The function f ( x ) = e x and find the location of the graphs of f ( x ) = e x − 4 , f ( x ) = e x − 6 , and f ( x ) = e x + 5 . Graph all three functions on the same set of axes with f ( x ) = e x .

Solution Summary: The author explains how to graph the function f(x)=ex.

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To graph:

The function f(x)=ex and find the location of the graphs of f(x)=ex−4, f(x)=ex−6, and f(x)=ex+5. Graph all three functions on the same set of axes with f(x)=ex.

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Chapter 11 Solutions

To graph: The function f ( x ) = e x and find the location of the graphs of f ( x ) = e x − 4 , f ( x ) = e x − 6 , and f ( x ) = e x + 5 . Graph all three functions on the same set of axes with f ( x ) = e x .

Solution Summary: The author explains how to graph the function f(x)=ex.

Concept explainers

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To graph: The function f(x)=ex and find the location of the graphs of f(x)=ex−4, f(x)=ex−6, and f(x)=ex+5. Graph all three functions on the same set of axes with f(x)=ex.

Want to see the full answer?

Chapter 11 Solutions

To graph:

The function f(x)=ex and find the location of the graphs of f(x)=ex−4, f(x)=ex−6, and f(x)=ex+5. Graph all three functions on the same set of axes with f(x)=ex.