Question

2. The graph of a function, f(x), is provided to the right. 2 Use this graph to answer each of the following questions. (a) You are also told that f(x) passes through (1, 0.8). -4-3-2f11 1 2 3 Find the equation of f(x), where you use the smallest degree possible. -2 (You can write your answer in factored form.) [6 pts] -3 -4 -5 -6 -7 -8 -9 (b) Based on the graph, describe the end behaviors of f(x). [2 points] (c) Does the graph have an inverse function? State “Yes” or “No” and then explain your answer. [4 points)

Answer 1

to Q2 The graph of a function, f(x), is provided. Use the graph answer each of the following questions (a) you are also told that f(x) passes through (1,0.8) find the equation of fl»). use the smallest degree possible where you X=-3 is the Solution is in the Graph The x- - intercept solution of the equation (x+3) = -0. The graph passes directly through the x- intercept at X=-3. The factor is lineas ( has a degree of 1), so the behavior hear the intocept is like that a line. The x-intercept is and X=0 L = -1 the solution of the equation (x+1)= 0 . The factor is linear, so the behavior near the intercept is like that a line The x-intercept is the solution of the equation is the repeated solution to the equation (2-0) The graph touches the axis at the intercept and Changes direction. The factor is quadratic (degree 2). So the behavior near the intercept is like that a quadratic It bounces off the horizontal axis at the inter copt.

The the equation X - intercept X=2 is the repeated solution of (x-2) = 0 The graph douches the axis at the intercept and Changes direction. then f(x) a (x+3)(x+1) (8-0)} (x-2)? ر۔ where is Shortch facter Criven f(1) 0,8 than put the car i 0.8 = a (1+3)(1+1) (1) (1-2) 0,8 ax 4xxx as 0.8 0.1 1 10 8 Put the value of a in equation à f(x) = 0.1*** (+1)(x+3)(x-2)} f(x) 1 x'(x+1)(x+3)(x-2) lo

4 on (b) Based the graph the end point behaviors of f(x) solution positive Leading coefficient X an>o I >o lo End behavior: xo, F(x) X-001 f(x) is and the Because This Even Degree (x) "function leading coefficient is positive, the graph rises to the left side to the right side as and gises Shown in the figure c) Docs the graph have an inverse function ? Answer is "NO" solution as because - Domain of f(x) = (-0,0) Range of f(x) = -9.5,-) in the graph for Given function every input value like (x=0, x=-1, x=-} and X = 2) than a mut Unique output is zero function is many- than anverse of function is not possible Condition of Inverse - function function is one-one onto has -One must

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