Use the method of partial fractions to find the inverse transforms of the functions: 1. F(s) = 2 s(S-1)(s+1) Find f(t):
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Use the method of partial fractions to find the inverse transforms of the functions:
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- Consider the function y = (1x + 1)x. (a) Differentiate y by the product rule. (b) First, multiply out the expression for y then differentiate.Sketch f(x)=c/x-2+3 on the same coordinate plane for the following 3. 1 values of c=-1,÷,5. (Make use of shifting, 2 stretching, compressing such as shrinking or reflecting).List the transformations that are applied to f(x)=Vx to produce f(x)=-/2(x+3) – 4
- [22] Express the function as a product by factoring the right-hand side: f (x) = x' + x² - 4x –4.Differentiate the function y = (3x)²(x – 3)³ with respect to x using product rule. Simplify your answer.The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. %3D where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) = f() The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 4 -6 -5 -4 -3 -2 -1 2. 4 5 6 -2 -3 -4 -5 Clear All Draw: Dot Line Segment
- The transformation of a function f(x) into a function g(a) is given by g(a) = Af(Bx + H) + K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(z) where the transformation is g(a) = f(# – 1) + 3 The function f(E) is shown below in red. Graph the transformed function g(z) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Transform the function by applying the constants in this order: H, B, A, K.) 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -3 -4 -5 Clear All Draw: Dot Line Segment Check AnswerThe transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) B horizontally scales the function. (negative Breflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(æ) = f(x – 3) – 1 The function f (x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Transform the function by applying the constants in this order: H, B, A, K.) 4 2 -6 -5 -4 -3 -2 -1 -1 I 2 3 4 5 6 -2 -3- -4 -5- Clear All Draw: Dot Line Segment 3.For the function f(x)= x+5, what is the odored pair for the point on the graph where x = 4w
- The sum of two positive numbers is 95. Find a function that models their product P in terms of x, one of the numbers. P(x) =y = x²e¬x . x+3' calculate the value of y for the following values of x, For the function 0, 1, 2, 3, 4, 5, 6, using element-by-element operations.The transformation of a function f(x) into a function g(x) is given by g(x) Af(Bx + H) + K. %3D where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) f(x) + 1 The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 6- 4 -6 -5 -4 -3 -2 -1 3. 4 5 6 -2 -3 -4 -5 -6+