1. The graph of a function and the graph of its inverse always have symmetry across * the x-axis the y-axis the line y = x O the line y = -x

Q: 2. The signum function denoted by sgn (x) read as "signum of x" is a function defined by sgn (x) =…

A: The equation of the basic equation of the function is given as sgn (x), that is shown below-…

Q: a)Find the inverse of f(x)=x+1. Graph ?and its inverse together. Add the line ?=?on the same sketch.…

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Q: The graph of the increasing differentiable function f is shown above. Also shown is the line tangent…

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Q: 1. The graph of function f(x) is shown below. y f(x) (a) By using the graph of f, explain how we…

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Q: 2. The graph of a function and its inverse are symmetric with respect to the line 3. If no…

A: An inverse of a function is a function that reverses the function back to its function variable. For…

Q: 6) A function y =e-2x is defined numerically for some data range x. It can be entered using: (а) у -…

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Q: Which of the following are true about a one-to-one function?  Select all that apply.   The graph…

A: Function is the relation between two sets such that one of the set has unique image in other set.…

Q: 1. The graph of a function y=f(x) always crosses the y-axis. True or False2. Every graph represents…

A: The given statement is true if 0 is included in the domain of the given function.And the given…

Q: 12. Which of the following is true about the graph of the function, y= (x-2)³(x-1)*(x+4)? A. The…

A: Given function is  y=x−23x−14x+4

Q: 4. if x -3 8 Step 1 of 3: Identify the general shape and direction of the graph of this function on…

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Q: A one-to-one function is given. 1 f(x) = 1--x Find the inverse of the function. Graph both the…

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Q: Please answer the question and show the solution (do note that there are two parts to the question).

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Q: 1. Consider the graph of a function. Graph its inverse on the blank template. to 3 2 1 lio -3 -2 1 2…

A: Solution:

Q: 2. Sketch the graph of the following piecewise function x E (-∞, –3) -1 * + 2 -3 2 Let g(x) = -…

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Q: Q#3. For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and…

A: If a curve is symmetric about the x-axis, the points (x,y) and (x,-y) mustlie on the curve. Hence,…

Q: 1) Graph the function f by starting with the graph of y = x² and using transformations. f(x) =(x –…

A: If f(x)=x2 Now we know that if graph of f(x) is transformed to f(x-a) then we shifts the graph of…

Q: Q. No. 2 a) Sketch the graph of function f(x) (2x-3 if -3SI<0 S(x) ={r if OSI<2 2sr55 if

A: the given function is: fx=2x-3     if   -3≤x&lt;0x2           if  0≤x&lt;2x          if  2≤x≤5 we…

Q: a. Find the inverse of ƒ(x) = x + 1. Graph ƒ and its inverse together. Add the line y = x to your…

A: The given function  is

Q: 2. Graph the function f (x) = 5(0.5)- and its reflection about the line y=x on the same axis, and…

A: Inverse of functions: If f and g are two functions which satisfies (f∘g)(x) = x = (g∘f)(x) then f is…

Q: Select the correct graph of the pair of functions on the same axis. f (x) = et and g (x) = In (x)…

A: Given: f(x)=ex   and   g(x)=ln(x) Where the function is f(x)=ex is the solid blue curve and…

Q: 2. The graph of f is shown in the figure. Sketch a graph of the derivative of f. y 8 10. 6 4 2 - 6…

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Q: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: (4) A function can sometimes be its own inverse. For instance f(r) = = -I and g(x) 1/x are both…

A: Let the example of inverse function be y=ex. Take logarithm on both sides of the equation y=ex and…

Q: The graphs of the functions f and g in the figure are obtained by vertical and horizontal shifts and…

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Q: 9. Let f be a function with f (2) = -5 such that for all points (x, y) on the graph of f the slope…

A: Solution: The objective is to find tangent equation

Q: 1.5 When a function f is even, then for every point (x, y) on the graph of fhere exists another…

A: If the given function is even or odd, you have to put the value of x is -x after the application if…

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

A: To sketch the approximate shape of the graph on the same axes.

Q: ax + b (x – 1)(x – 4) at point (2, – 1), determine the values of a and b. If the graph of the…

A: Given: g(x)=y=ax+b(x-1)(x-4) Since, the point (2,-1) is lying on the given curve. So, when x=2,y=-1.…

Q: 1 6 For f(x) = the slope of the graph of y = f(x) is known to be at the point with x-coordinate 3.…

A: Given: fx=12+x2 Point slope form of an equation of a line is: y-y1=mx-x1. Here, the line passes…

Q: A function f is given, and the indicated transformations are applied to its graph (in the given…

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Q: 2. The graph of a function defined for x 2 0 is given. Complete the graph for x < 0 to make an (a.)…

A: (a) The graph of the function defined for x≥0 is shown below,

Q: 3. Match the graph of each function in (a)–(d) with the graph of its derivative ih I-IV. Give…

A: Given, The graph of the function from (a), (b), (c), and (d) The graph of the derivative of the…

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 9/2 x +…

A: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 9/2 x…

Q: Question 4 If f and g are the functions whose graphs are shown, let h(a) =9(f(x)). Find h'(1). -2…

A: First we find h'(x).

Q: 4. The graph of f(x)=√√x is compressed vertically by a factor of 1/2, compressed horizontally by a…

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Q: -12-1110 -9 8 -7 6 5 3. 8 9 10 11 12 -2 -3 -5 Give the equation for the function whose graph appears…

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Q: 1. Sketch a graph of the function f given by f(0) = 2sin(0). y 4 1 + -1 4 -2 -3 3. 2.

A: This question is based on graphing a trigonometric function value at specific angle and by joining…

Q: 4 if x -3 Step 1 of 3: Identify the general shape and direction of the graph of this function on…

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Q: Let P = (x, y) be a point on the graph of y = √x.(a) Express the distance d from P to the point (1,…

A: The graph given to us is y = √x.

Q: a. Are f(x) = x19 and g(x) = x inverses of each other? b. Graph fand g over an x-interval large…

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Q: For tho the function F whose graph is given state the value of the given quantity if it exists (if…

A: THE EXPLANATION HAS BEEN GIVEN IN TYHE ATTACHED  FILE .

Q: 4 if x < -3 k(x) = Vĩ if x 2 -3 2 of 3: Identify the general shape and direction of the graph of…

A: On the interval [-3, infinity) k(x) = (7/8)(x)1/3

Q: function f is given, and the indicated transformations are applied to its graph (in the given…

A: Equation of final transformation is given with graph.

Q: Find the equation of the line tangent to the graph of the given function at the point with the…

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Q: 7. Graph the piecewise defined function f by ans (x²-1 if-3<x<1 if x = 1 2-x if 1<x<5 f(x) = { 3 a.…

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Q: Ignore my work

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Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H)+ K. where…

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Q: 1. The graph of the function f (x) = |x| is transformed by a vertical stretch by a factor of a…

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Q: The graph of the function y = x4 is transformed to the graph of the function y = –2(x – 3)4 + 1 by…

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Q: Which of the following statements is not true? 1) The graph of an odd function is symmetrical about…

A: 1. As when graph of a function is symmetric about y-axis then it is an even function. But in option…