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Math 101 Hour Exam II Name__________________________________________ 1. Find the linear equation: a) joining the points (4, −2) and (3, 5). b) determined by the function values f(5) = 1 and f(7) = 0. 2. A cable television company charges a $85 installation fee and $70 per month for service. Write an equation for the total cost for t months of service and calculate the cost of a full year of service. 3. Find the relative maximum and/or minimum of the function G(x) = 4x − 4x 3 and the interval(s) on which G(x) is increasing, decreasing, or constant. Maximum______________________ Minimum_______________________ G(x) is increasing on the interval(s)_______________________________ G(x) is decreasing on the interval(s)_______________________________ G(x) is constant on the interval(s)_________________________________ 3. Let f(x) = x 2 – 4 and g(x) = x . Find and simplify: 2x + 6 a) (f – g)(−2) b) (f ∘ g)(0) c) (g ∘ f)(x) d) The domain of g(x) in interval notation e) The domain of f(x) in interval notation 4. Simplify the difference quotient f (x + h ) − f (x ) when f(x) = x 2 + 2. h 5. Find the equation of a function which resembles y = 1 shifted right 3 units and x down 7 units. 6. Sketch a graph of the function f(x) = 4x − 6, x ≤ 3 3 − x, x > 3 Label at least 3 points. 7. Use algebra to determine if the graph of the function y = 4x shows symmetry to 1− x the x-axis, the y-axis, the origin, or none of these. 8. Find the equation of a line passing through (3, −2) which is parallel to the line 2x − 6y = 1.