Chapter 3 Practice test #1 –2: Determine the domain and range of each function, write your answer in interval notation when appropriate. 1) 2) 3) 4) #5-7: Use algebra to find the domain of each function. Write your answer in interval notation. 5) 𝑓(𝑥) = 𝑥−4 𝑥 2 +3𝑥+2 6) 𝑓(𝑥) = √𝑥 − 6 7) f(x) = x2 – 16 #8– 10: let f(x) = 2x + 5 and g(x) = 3x – 1, find the following 8) (𝑓 − 𝑔)(𝑥) 9) (𝑔 ∘ 𝑓)(𝑥) #8– 10: let f(x) = 2x + 5 and g(x) = 3x – 1, find the following 10) (f+g)(2) 11) Find the difference quotient; that is find 𝑓(𝑥+ℎ)−𝑓(𝑥) ℎ ; f(x) = 2x – 3 12) Find the average rate of change of f(x) = x3 + 6x2 from 0 to 2 𝑥 + 5, 𝑖𝑓 𝑥 ≤ 2 13) g(x) = {𝑥 + 6, 𝑖𝑓 2 < 𝑥 ≤ 5 5𝑥 𝑖𝑓 𝑥 > 5 2 a) g(2) b) g(6) c) g(5) 14) Use the graph below to answer the following: (call the function graphed below f(x)) 14a) Find f(2) 14b) Find f(-6) 14c) Find all values of x such that f(x) = 2 14d) Find all values of x such that f(x) = -6 15) Use the graph below to answer question the following: 15a) the interval(s) where the function graphed is increasing 15b) the interval(s) where the function graphed is decreasing 15c) The values of x (if any) where the function has a local maximum 15d) The local maximum value (if any) 15e) The values of x (if any) where the function has a local minimum 15f) The local minimum values (if any) #16 - 20 let 𝑓(𝑥) = 𝑥 2 a) find the requested function b) describe the transformation from the original function. 16a) 𝑓(𝑥 − 3) 16b) 17a) −𝑓(𝑥 + 5) 17b) 18a) 𝑓(𝑥) + 2 18b) 19a) 𝑓(𝑥 + 2) − 4 19b) 20a) 𝑓(𝑥 − 1) + 7 20b) 21) A campground owner has 2000 meters of fencing. He wants to enclose a rectangular field bordering a river, with no fencing needed along the river, and let W represent the width of the field. a) Write an equation for the length of the field b) Write an equation for the area of the field. c) Find the value of w leading to the maximum area d) Find the value of L leading to the maximum area e) Find the maximum area. Up and down shifts Transformation y = f(x) + k (k>0) Shift the graph UP k units Y = f(x) – k (k>0) Shift the graph DOWN k units Left and right shifts Transformation y = f(x+h) (h >0) Shift graph LEFT h units y = f(x-h) (h>0) Shift graph RIGHT h units Reflections Transformation y= -f(x) REFLECTS graph about x-axis y= f(-x) REFLECTS graph about y-axis Compressing and stretching Transformation y = af(x) (a >0) STRETCHES the graph when a>1 COMPRESSES graph when 0 < a < 1