C
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|Name___________________Score_____ |Name_____________________Score_____ |
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|Calculus Warm-up # 1-A |Calculus Warm-up # 1-B |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|1) Find the domain of the function |6) Find the value of [pic] _________ |
|f(x) = [pic] ________ | |
| |7) True or False? [pic] = -5 _________ |
|2) ) Find the domain of the function | |
|f(x) = [pic] ________ |8) Find the domain of the function |
| |y = [pic] _________ |
|3) For what value of x is the function | |
|y = [pic] undefined? ________ |9) Find the domain of the function |
|4) What is the y-intercept of the graph of |y = [pic] _________ |
|the function y = [pic]? ________ | |
|5) True or False? -32 = | -32| ________ |10) Find the range of the function |
| |y = 2x. ________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 1-C |Calculus Warm-up #1-D |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|11) If f(x) = x2 – 7x + 12, find f(-5). |16) At what point, besides the origin, do the |
|________ |graphs of y = x2 and y = x3 intersect? |
| |________ |
|12) If f(x) = (x – 3)(x – 4), find f(12). |17) True or False? If x is any Real number, |
|________ |then [pic] is also a Real number. |
| |________ |
|13) Find the domain of the function |18) Find f(5) if f(x) = x2 – 8x + 15 |
|y =[pic]. ________ |________ |
| | |
|14) Find the domain of the function |19) Find f(5) if f(x) = (x – 3)(x – 5) |
|y =[pic]. ________ |________ |
| | |
|15) For what values of x is the function |20) True or False? If x = -3, |
|f(x) = [pic] undefined? ________ |then [pic] = | x - 1| ________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 2-A |Calculus Warm-up # 2-B |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|1) Find the domain of the function |6) True or False? If x > π/2, then |
|f(x) = [pic] ________ |sin 12x > 1. _________ |
| | |
|2) ) Find the domain of the function |7) True or False? [pic] is a reflection |
|f(x) = [pic] ________ |of the sine graph about the x-axis. _________ |
|3) True or False? If [pic], then [pic] | |
|is always positive. ________ |8) For what value of x is the function |
| |f(x) = [pic] undefined in the interval |
|4) For what value of x is the function |[π/2, 3π/2] ? _________ |
|f(x) = [pic] undefined? ________ | |
|5) sin ( 7π/6) = ________ |9) Find the domain of the function |
| |[pic] _________ |
| | |
| |10) cos (3π/2) = ________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 2-C |Calculus Warm-up # 2-D |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|11) On what interval is the function |16) Find the value of (-8)1/3 _________ |
|[pic] defined? _________ | |
| |17) Multiple Choice. |
|12) Find the x-intercept of the function |What is the value of -41/2? |
|[pic] ____________ | |
| |A. -2 B. dne C. 2 D. -1/2 |
|13) Find the slope of the line whose |________ |
|equation is 6x + 3y = 11. __________ |18) True or False? Given that y = 1/x, |
| |if x > 100, y < .01 _________ |
|14) Find the slope of the line that goes | |
|through (7, 2) and (-1, 0) __________ |19) Multiple Choice. How does the graph of |
| |f(x) - 7 compare to the graph of f(x)? |
|15) tan (3π/4) = _________ |A. slide 7 units up B. slide 7 units left |
| |C. slide 7 units down D. slide 7 units right |
| |________ |
| |20) csc (2π/3) = ________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 3-A |Calculus Warm-up # 3-B |
|NO CALCULATORS TODAY |NO CALCULATORS TODAY |
| | |
|1) sin (-3π/2) ________ |6) True or False? If f and g are nonzero |
| |functions, then f(g(x)) = g(f(x)). |
|2) Is the function f(x) = 6x2 a one-to-one |_________ |
|function? ________ |7) At how many points do the graphs of |
| |y = 3x3 + 1 and y = 3x3 + 6 intersect? |
|3) Find the inverse of the function |_________ |
|f(x) = x2 + 5, where x ≥ 0 ________ |8) For what value of x between π and 3π is |
| |[pic] undefined? _________ |
|4) Find the domain of the function | |
|[pic] ________ |9) Write the equation of the line with slope |
|5) Find the y-intercept of the graph of |7 that passes through the point (6, -2). |
|y = ex + 5 ________ |_________ |
| |10) Simplify: [pic] _________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 3-C |Calculus Warm-up #3-D |
|NO CALCULATORS TODAY |CALCULATORS ARE ALLOWED |
| | |
|11) If f(x) = [pic], find f(3). |16) Is the function [pic] |
|________ |an even function, an odd function, or |
| |neither? ________ |
|12) Find f(-3) for the function above. |17) Is the above function one-to-one? |
|________ |________ |
|13) Is the function referred to above an |18) If the graph of f(x) = x2 is shifted two |
|even function, an odd function, or |units to the right to form g(x), what |
|neither? ________ |would be the equation of g(x)? |
| |________ |
|14) sec (2π/3) ________ | |
| |19) Write the equation of the line through |
|15) Find the vertical asymptote of the |the point (-9, 2) that is parallel to |
|graph of the function [pic] |2x – 5y = 16 ________ |
|________ | |
| |20) Simplify: (x – 2y)2 – (xy2 – y2) |
| |________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 4-A |Calculus Warm-up # 4-B |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|1) sin (π/2) ________ |On # 6-9, Solve for x, when 0 ≤ x < 2π |
| | |
|2) cos (3π/4) ________ |6) cos x = 0 _________ |
| | |
|3) tan (-π/4) ________ |7) sin x = -1/2 _________ |
| | |
|4) sec (π/3) ________ |8) sec x = 2 _________ |
| | |
|5) Simplify: |9) tan x = 1 _________ |
|(2x2)3 | |
|x10 ____________ |10) Find the domain of y = [pic] |
| |___________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 4-C |Calculus Warm-up # 4-D |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|11) tan (5π/4) _______ |On #16-18, solve for x when 0 ≤ x < 2π. |
| | |
|12) cos (-π) _______ |16) sin x = [pic] _________ |
| | |
|13) csc (π) _______ |17) cos x = [pic] _________ |
| | |
|14) sin ( -5π/3) _______ |18) csc x = -1 _________ |
| | |
|15) Does y = │x3 - x│ have even or |19) What is the domain of y = tan x? |
|odd symmetry? ___________ |___________ |
| | |
| |20) Write the equation of the line |
| |through (9, -4) and ( -1, 5) |
| |___________________ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 5-A |Calculus Warm-up # 5-B |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|1) [pic] ________ |6) Find f(4) if f(x) = x + 5 _________ |
| | |
|2) [pic] ________ |7) Find f(4) if f(x) =[pic] ________ |
| | |
|3) [pic] ________ |8) For what value of x is f(x) = [pic] |
| |undefined? _________ |
|4) [pic] ________ | |
| |9) [pic][pic]= _______ |
|5) Write the equation of the vertical line | |
|through the point (-6, 8). |10) [pic][pic]= _______ |
| | |
|________________ | |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 5-C |Calculus Warm-up # 5-D |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
| |16) Is the function y = [pic] continuous |
| |at x = 7.2. _________ |
| |17) Is f(x) = [pic] continuous |
| |at x = 2? __________ |
|11) [pic] = _______ | |
| |18) Is the function y = │x - 2│ continuous |
|12) [pic] = _______ |at x = 2 ? __________ |
| | |
|13) True or False?[pic] does not exist. |19) Is the function y = [pic] continuous |
| |at x = 2? __________ |
|14) [pic] = _______ | |
|15) True or False? [pic] = [pic] |20) [pic][pic] = _______ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 6-A |Calculus Warm-up # 6-B |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|1) [pic] _______ |6) [pic] ________ |
| | |
|2) [pic] _______ |7) [pic] ________ |
| | |
|3) [pic] _______ |8) [pic] _________ |
| | |
|4) [pic] ________ |9) [pic] _______ |
| | |
|5) [pic] ___________ |10) Multiple Choice: [pic] |
| |A. -14 B. 49 C. [pic] D. [pic] |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 6-C |Calculus Warm-up # 6-D |
|NO CALCULATORS THIS WEEK! |NO CALCULATORS THIS WEEK! |
| | |
|11) True or False? |16) What is the slope of a line perpendicular |
|The function f(x) = [pic] approaches |to the line 3y + 5x = 10? ______ |
|98 as x approaches 7. | |
| |17) [pic] ______ |
|12) [pic] ______ | |
| |18) What is the image of the point (-2, 7) |
|13) [pic] ______ |when it is reflected across the x-axis? |
| |_______ |
|14) [pic] ______ | |
| |19) Multiple Choice: [pic] |
|15) Find the slope of a line perpendicular |A. [pic] B. [pic] C. [pic] D. [pic] |
|to the line y = 6x – 1. ______ | |
| |20) Find the y-intercept of the function |
| |g(x) = 5 cos 2x _______ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 7-A |Calculus Warm-up # 7-B |
|NO CALCULATORS TODAY! |NO CALCULATORS TODAY! |
| | |
|1) Find the domain of the function |6) [pic] _______ |
|f(x) =[pic] _______ | |
| | |
|2) Does the graph of y =[pic] have a hole |7) [pic] _______ |
|or an asymptote at x = 3? _______ | |
| | |
|3) Does the graph of y =[pic] have a hole |8) [pic] _______ |
|or an asymptote at x = 4? _______ | |
| | |
|4) True or False? The function y =[pic] is |9) [pic] _______ |
|undefined when x = -1/2. _______ | |
| |10) If [pic], find y’. ____________ |
|5) If [pic], find y’. _______________ | |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 7-C |Calculus Warm-up # 7-D |
|NO CALCULATORS TODAY! |USE YOUR TI-89 TODAY! Round to 3 decimal places. |
| | |
|11) [pic] ______ |Let f(x) =[pic] |
| | |
| |16) Find [pic] _______ |
|12) [pic] ______ | |
| | |
| |17) Find [pic] _______ |
|13) [pic] ______ | |
| | |
| |18) Find [pic] _______ |
|14) [pic] ______ | |
| | |
| |19) Find [pic] _______ |
|15) If [pic], find [pic] | |
|____________ | |
| |20) Find [pic] _______ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 8-A |Calculus Warm-up # 8-B |
|NO CALCULATORS TODAY! |NO CALCULATORS TODAY! |
| | |
|1) If u = 3x4, find [pic] _______ |6) If u = 6x5, find [pic] _______ |
| | |
|2) If v = 5x3, find [pic] _______ |7) If v = 3x3, find [pic] _______ |
| | |
|3) Multiply u ∙ v, and simplify it. |8) Find [pic], and simplify it. |
|Call the product y. y = _______ |Call the quotient y. y = _______ |
| | |
|4) Find [pic] _______ |9) Find [pic] _______ |
| | |
|5) Multiply [pic] and[pic] from # 1 and # 2. |10) Is it true that [pic]? _______ |
|Is it true that (uv)′ = (u′)(v′)? ______ | |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 8-C |Calculus Warm-up # 8-D |
|NO CALCULATORS TODAY! |USE YOUR TI-89 TODAY! Round to 3 decimal places. |
| | |
|11) Where does the graph y =[pic] have |Given f(x) = [pic] |
|a hole? _________ | |
| |16) Find [pic] _______ |
|12) Write the equation of the tangent line | |
|to y = x3 – 4x at the point (1, -3). | |
|_________ |17) Find [pic] _______ |
| | |
|13) Find the slope of the tangent line to | |
|y = 2x4 + x – 1 where x = 2 ______ |18) Find f (ln 2) _______ |
| | |
|14) Find the slope of a line which is | |
|parallel to the line 2y = 7x - 6 ______ |19) Find f ′ (ln 2) _______ |
| | |
| | |
|15) Find the y-intercept of the graph of |20) Find f ′′ (ln 2) _______ |
|f(x) = 3x5 + x4 – 2x3 -7x + 6 ______ | |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 9-A |Calculus Warm-up # 9-B |
|NO CALCULATORS TODAY! |NO CALCULATORS TODAY! |
| | |
|1) Find [pic] if [pic][pic][pic] _______ |6) Find y ′ if [pic] _______ |
| | |
|2) Find [pic] if [pic][pic][pic] _______ |7) Find y ′ if [pic] _______ |
| | |
|3) Find [pic] if [pic][pic][pic] _______ | |
| |8) Find y ′ if [pic] _______ |
|4) Find [pic] if [pic] _______ | |
| | |
|5) What is the vertical asymptote of the |9) Find y ′ if [pic] _______ |
|function [pic] ? _______ | |
| |10) The graph of f(x + 4) is a translation of |
| |the graph of f(x) 4 units in which |
| |direction? _______ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 9-C |Calculus Warm-up # 9-D |
|NO CALCULATORS TODAY! |USE YOUR TI-89 TODAY! Round to 3 decimal places. |
| | |
|11) Find [pic] if [pic][pic][pic] _______ |16) True or False? For all x, |
| |[pic] _______ |
|12) Find [pic] if [pic][pic][pic] _______ | |
| |17) Find the domain of the function |
|13) Find [pic] if [pic][pic][pic] _______ |[pic] _______ |
| | |
|14) Find [pic] if [pic][pic] [pic] _______ |18) Find [pic] if [pic] _______ |
| | |
|15) Find the slope of the curve |19) Find [pic] _______ |
|[pic] where x = -2 _______ | |
| |20) Find the slope of the curve |
| |[pic] where x = 1 _______ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 10-A |Calculus Warm-up # 10-B |
|NO CALCULATORS TODAY! |NO CALCULATORS TODAY! |
| | |
|1) Find [pic] if [pic][pic][pic] _______ |6) Find y ′ if [pic] _______ |
| | |
|2) Find [pic] if [pic][pic][pic] _______ |7) Find y ′ if [pic] _______ |
| | |
|3) Find [pic] if [pic][pic][pic] _______ | |
| |8) Find y ′ if [pic] _______ |
|4) Find [pic] if [pic] _______ | |
| | |
|5) What is the domain of the function |9) Find y ′ if [pic] _______ |
|[pic]? ________ | |
| |10) What is the y-intercept of the graph |
| |of [pic]? _______ |
| | |
|Name___________________Score_____ |Name_____________________Score_____ |
| | |
|Calculus Warm-up # 10-C |Calculus Warm-up # 10-D |
|NO CALCULATORS TODAY! |NO CALCULATORS TODAY! |
| | |
|11) Find [pic] if [pic][pic][pic] __________ |16) Find [pic] _______ |
| | |
|12) Find [pic] if [pic][pic][pic] _________ |17) Find [pic] _______ |
| | |
|13) Find [pic] if [pic][pic][pic] __________ |18) Solve: [pic] [pic]_______ |
| | |
|14) Find [pic] if [pic][pic] [pic] ___________ | |
| | |
|15) Write the equation of the tangent line |19) Solve: [pic] _______ |
|to the curve [pic] at [pic] | |
|____________ | |
| | |
| |20) What is the domain of[pic]? |
| |_______ |
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