Use graphs to determine if each function f in Exercises 45–48is continuous at the given point x = c.[2 – x, if x rationalx², if x irrational,45. f(x)c = 2x² – 3, if x rational46. f(x) = { 3x +1, if x irrational,c = 0[2 – x, if x rational47. f(x) = { x², if x irrational,c = 1x² – 3, if x rational3x +1, if x irrational,48. f(x) :c = 4

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Answered: Use graphs to determine if each…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

Suppose that Af is the function given by the graph below and that da and a + ha + h are the input values as labeled on the bex – axis. Use the graph in Figure 1.3.2 to answer the following questions. Locate and label the points (a, f(a))(a, f(a)) and Ka + h, f(a+h)X(a +h, f(a + h)) on the graph. D. Construct a right triangle whose hypotenuse is the line segment from (a, f(a))(a, f (a)) to Ka + h, f(a + h)Xa + h, f(a + h)). what are the lengths of the respective legs of this triangle? C What is the slope of the line that connects the points (a, ƒ (a))(a, ƒ (a)) an Ka + h, f(a+ h))Xa +h, f(a+ h))?
In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16
The graph of which function has an axis of symmetry at x = O fx) = 2x2 + x-1 O fx) = 2x2-x+ 1 O fix) = x2 + 2x-1 O fx) = x2 - 2x + 1
Suppose that f and g are both odd. Which of the following functions are even? ☐ y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x) ¹3 Which of the following functions are odd? y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x)¹3
Identify the inner and outer functions in the composition (6x? +7) * Let f(u) represent the outer function and g(x) represent the inner function.
Define f (x) = x+3 Identify which of the following are points on the graph of this function (identify ALL correct answers!). A) (-0.5,0.2) B) (1,0.25) C) (-2,-2) D) (5,0.625) E) (-1,2) F) (0,3)

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