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practice_exam_3

# practice_exam_3 - f is below the x-axis(iv Find the power...

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Math 140 Section B2 Spring 2007 Practice Exam III Instructor: Atilla Sit 1. Graph the piecewise-deﬁned function f ( x ) = | x | if - 2 x < 0 1 if x = 0 x 3 if x > 0 Based on the graph: (a) Find the domain of f . (b) Find the range of f . (c) Locate any intercepts. 2. Graph the function f ( x ) = x 2 + 4 x by using shifting techniques and showing all stages. Be sure to locate the vertex and any intercepts on the ﬁnal graph. ( Hint: Complete the square and transform the equation into f ( x ) = ( x - h ) 2 + k ﬁrst). 3. Find the equation of the quadratic function having vertex at ( - 3 , 5) and passing through (0 , - 4). 4. Analyze and sketch the graphs of following functions by performing the given steps: (a) f ( x ) = - 2 x ( x - 1) 2 ( x - 2). (i) Find all the intercepts. (ii) Determine whether the graph crosses or touches the x -axis at each x -intercept. (iii) Use x -intercepts to ﬁnd the intervals on which f is above the x -axis and the intervals on which
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Unformatted text preview: f is below the x-axis. (iv) Find the power function that the graph of f resembles for large values of | x | . (v) Sketch the graph of f . (b) f ( x ) = 2 x x 2-x-2 . (i) Find the domain of f . (ii) Find all the intercepts. (iii) Check for symmetry. (iv) Find all vertical asymptotes (if any). (v) Find all horizontal asymptotes (if any). If there is a horizontal asymptote diﬀerent than x-axis, check whether it crosses the graph of f or not. (vi) Use x-intercepts and the points not in the domain of f to ﬁnd the intervals on which f is above the x-axis and the intervals on which f is below the x-axis (vii) Sketch the graph of f . 5. Solve the inequality x-4 2 x + 4 ≥ 1 . Write the solution set in interval notation....
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