Calculus P - Review Review Problems

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Review Problems Given x 2 + x 28

Review Problems Find the x-intercept(s): 3x 2 + 2y 2 + 4xy - 12 = 0. ±2 29

Review Problems Find the x-intercept(s): y = 2x

Review Problems Find the x-intercept(s): y = x 3 (x + 2)(3x - 1) (0, 0), (-2, 0), (1/3,0) 31

Review Problems Find the intercepts:. (0,-1/3), (1/2,0) 32

Review Problems Identify the type(s) of symmetry: x 4 y 2 + 2x 2 y - 1 = 0 To y-axis Identity the type(s) of symmetry: y = x 3 + 3x To origin 33

Review Problems Identify the type(s) of symmetry: y = |x| - 2 Symmetric to the y-axis 34

Review Problems Determine if is symmetrical with respect to the x-axis, the y-axis, or the origin. About the y-axis 35

Review Problems Find all points of intersection of the graphs of x 2 + 3x - y = 3 and x + y = 2 (-5, 7), (1, 1) Find all points of intersection: y = -x 2 + 4x and y = x 2 (0, 0), (2, 4) 36

Review Problems Find the number of sales necessary to break even for the cost C of x units and the revenue R obtained by selling x units if C = 3000x and R = 3250x

Review Problems If the point (-1, 1) lies on the graph of the equation kx 2 - xy + y 2 = 5, find the value of k 3 38

Review Problems Find the slope of the line passing through the points (-1, 16) and (4, 2). Find the slope of a line that is perpendicular to the line given by 2x + 3y + 9 = 0 39

Review Problems Find the equation of the line that has a slope of and passes through the point (1, 2). 3x + 4y - 11 = 0 40

Review Problems Find the equation of the vertical line that passes through the point (2, 5). x = 2 Find the equation of the line that passes through the point (0, 0) and has a slope that is undefined x = 0 41

Review Problems Find the equation of the line that passes through the point (-1, 5) and has a slope of 2 2x - y + 7 = 0 Find an equation for the horizontal line that passes through the point (-3, 2) y = 2 42

Review Problems Find the domain:. All reals except 43

Review Problems Given f(x) = x2 - 3x + 4, find f(x + 2) - f(2). x 2 + x Given f(x) = |x - 3| - 5, find f(1) - f(5). 0 44

Review Problems Find f(x + Δx) for f(x) = x 2 - 2x - 3 x 2 + 2x(Δx) + (Δx) 2 - 2x - 2 Δx

Review Problems If g(x) = x 2 + 3x - 1, find. 2x + Δx + 3 Find if f(x) = 4x x + 4Δx 46

Review Problems Which of the following is a sketch of the graph of the function f(x) = x 3 + 1? I 47

Review Problems Given the graph of y = x 2, sketch the graph of y = (x + 3)

Review Problems Use the graph of y = x 2 to find a formula for the function y = f(x). f(x) = (x - 2)

Review Problems Use the graph of f shown below to sketch the graph of y = f(x)

Review Problems Describe the transformation needed to sketch the graph of using the graph of Shift f(x) two units upward 51

Review Problems Given f(x) = 6x - 12 and g(x) = x 2 - 4, find. 52

Review Problems If and find f(g(x)) 53

Review Problems If and find f(g(x)) 54

Review Problems If f(x) = and g(x) = find g(f( - 2)) 55

ANSWERS Graph 5. Graph 6. Graph 7. Graph

ANSWERS Graph 20. Graph Graph 24. Graph 25. Graph 26. Graph x 2 + x ±2 (0, 0), (-2, 0), (1/3,0) (0,-1/3), (1/2,0)

ANSWERS Graph To y-axis To origin Symmetric to the y-axis About the y-axis (-5, 7), (1, 1)(0, 0), (2, 4) x + 4y - 11 = 0 x = 2x = 0 2x - y + 7 = 0 y = 2 All reals except x 2 + x0 x 2 + 2x(Δx) + (Δx) 2 - 2x - 2 Δx - 3 2x + Δx + 3 8x + 4Δx I

ANSWERS Graph f(x) = (x - 2) Shift f(x) two units upward