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Problem 4 State whether false or true: The parabola is an even function. All functions are either even or odd. ~ TRUEX i) TRU E/ ii) iii) For any function f(x), –f(x – 5) – 1 shifts the graph horizontally to the left by five units, compresses the graph vertically by the factor 3 and shifts the graph downward by one unit, in this order. - TPUEX Supnose E(4)

Problem 4 State whether false or true: The parabola is an even function. All functions are either even or odd. ~ TRUEX i) TRU E/ ii) iii) For any function f(x), –f(x – 5) – 1 shifts the graph horizontally to the left by five units, compresses the graph vertically by the factor 3 and shifts the graph downward by one unit, in this order. - TPUEX Supnose E(4)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 47E
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Problem 4 State whether false or true: i) The parabola is an even function. TRU E ii) All functions are either even or odd. ~ TRuEX iii) For any function f(x), ÷f(x – 5) – 1 shifts the graph horizontally to the left - by five units, compresses the graph vertically by the factor 3 and shifts the graph downward by one unit, in this order. - TPUEX iv) Suppose f(t) = t². Then f(t+h) = t² + h. - FALSE v) %3D %3D The slope of the tangent to the graph of a function in a particular point (x, f(x)) is given by the difference quotient 2, for any increment 4x. FALSE 4y TRUE The derivative of a function in a point (x, f(x)) is given, geometrically, as the slope of the tangent to the graph in that point. - TRUE vii) The derivative of the function f (x) viii) For an angle ©, the sin(0) function gives the ratio of the opposite side and the hypotenuse: sin(0) is an odd function with period 2n and is defined for all 0 € vi) = 2x² – 1 is equal to 4x. -TRUEV R. - TRUEV ix) If f(1) > 0 and f (3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0. – FALSE E If f is differentiable at a, then f is continuous at a.- %3D x)
Transcribed Image Text:Problem 4 State whether false or true: i) The parabola is an even function. TRU E ii) All functions are either even or odd. ~ TRuEX iii) For any function f(x), ÷f(x – 5) – 1 shifts the graph horizontally to the left - by five units, compresses the graph vertically by the factor 3 and shifts the graph downward by one unit, in this order. - TPUEX iv) Suppose f(t) = t². Then f(t+h) = t² + h. - FALSE v) %3D %3D The slope of the tangent to the graph of a function in a particular point (x, f(x)) is given by the difference quotient 2, for any increment 4x. FALSE 4y TRUE The derivative of a function in a point (x, f(x)) is given, geometrically, as the slope of the tangent to the graph in that point. - TRUE vii) The derivative of the function f (x) viii) For an angle ©, the sin(0) function gives the ratio of the opposite side and the hypotenuse: sin(0) is an odd function with period 2n and is defined for all 0 € vi) = 2x² – 1 is equal to 4x. -TRUEV R. - TRUEV ix) If f(1) > 0 and f (3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0. – FALSE E If f is differentiable at a, then f is continuous at a.- %3D x)
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