Question: In Problems 2530, answer the questions about each function. f(x) = x + 2 x + 4 (a) Is the point (1, 2) on the

In Problems 25–30, answer the questions about each function. f(x) = x + 2 x + 4 (a) Is the point

f(x) = x + 2 x + 4 (a) Is the point (1, 2) on the graph of f? (b) If x (c) If f(x) of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. (g) What are the zeros of f, if any? = 0, what is f(x)? What point is on the graph of f? 1 = =, what is x? What point(s) are on the graph

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Lets go through each question step by step a To determine if the point 1 35 is on the graph of fx we need to check if plugging x 1 into the function fx gives us y 35 fx x 2x 4 f1 1 21 4 f1 1 25 f1 1 25 f1 55 25 f1 75 The ycoordinate of the point 1 35 is 35 which is not equal to 75 Therefore the point 1 35 is not on the graph of f b If x 0 we can find fx by plugging x 0 into the function fx x 2x 4 f0 0 20 4 f0 0 24 f0 24 f0 12 When x 0 the point on the graph of f is 0 12 c To find the values of x when fx 12 we can set fx equal to 12 and solve for x fx 12 x 2x 4 12 This equation is a quadratic equation By rearranging and solving for x we get 2x 4 x 4 2x x 2x x 0 x2x 1 0 This equation has two solutions x 0 2x 1 0 2x 1 x 12 So when fx 12 the points on the graph of f are 0 12 and 12 12 d The domain of f is the set of all real numbers except the values that make the denominator of the fraction equal to zero In this case the denominator is x 4 So the domain of f is all real numbers except x 4 Domain of f 4 4 e To find the xintercepts of the graph of f we need to find the values of x for which fx 0 In other words we need to solve the equation x 2x 4 0 However this equation doesnt have any real solutions because the quadratic term x is always positive or zero and the fraction term 2x 4 is always positive or negative but it cant be zero Therefore there are no xintercepts for the graph of f f To find the yintercept of the graph of f we need to find the value of f0 f0 0 20 4 f0 0 24 f0 12 So the yintercept of the graph of f is 0 12 g The zeros of f are the values of x for which fx 0 As mentioned earlier the equation x 2x 4 0 doesnt have any real solutions Therefore there are no zeros for the function f ... View full answer

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