logarithmic function

1. Sketch the graph of the following piecewise function. Then answer the questions about the piecewise function. 1x-2 if x < -3 f(x) = Vx+4 if -3 0 5 if x = -3 6 7 8 9 X Domain: x-intercept(s):_ (written as a point) Range: y-intercept(s): (written as a point) 1 2. Find the domain of the following function. State your answer in interval notation. a) f(x) = Vx+3 x? – 5x-6 b)f(x) = ln(4x – 9) 3. Use the table below to answer the following questions. If the value cannot be determined from the table, state “UNDEFINED.” 1 3 X f(x) g(x) -2 -5 -1 -3 0 2 2 5 3 0 4 3 9 2 3 -2 (a) f(g(1)) (b) (gºf)(3) (c) x such that g(x) = 2 (d) (fºp(0) 2 4. Write an equation for the exponential function y = 10* function that has been reflected about the x axis and shifted horizontally to the right 8 units. Sketch the graph of this function and state the domain and range of this function. Make sure you label any asymptotes on your graph! 4 3 + -5 -3 -2 -1 1 2 3 4 5 Function: Domain: Range: y 5. Write an equation for the logarithmic function y = log,x function that has been reflected about the axis and shifted Vertically to the down 4 units. Sketch the graph of this function and state the domain and range of this function. Make sure you label any asymptotes on your graph! 4+ 3+ -5 4 -3 -2 2 3 4 Function: Domain: Range: 3 f(x+h)-f(x) 6. Evaluate the difference quotient, h for the following function: -9 f(x) = x + 3 1)- 7. a)What is the volume of a box where the length of the box is seven times the width? (See diagram)? Your answer will be in terms of x and y. 7x b) What is the surface area of the box where the length is seven times the width with no top (see diagram)? Your answer will be in terms of both x and y. 3 c)An open box with volume of 6m has the length of the box that is 7 times the width. Express the surface area of the box as a function of the length of the side of its base. 4 8. Solve the following equations for x. (a) 7e 3* 3x-1 = 9 (b) 2 log, (x – 1) – log, 9 = 2 9. Determine if the following are true or false. a) log logx – 3 logy a d) log b loga logb _b) log(a – b) = loga – logb e) (loga)(logb) = loga + logb f) 3 In(a + b) = ln(3a +36) loga = log(a – b) logb 5
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