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MHF4U 5.1 Learning Goal(s): Define trigonometric functions, graph primary trigonometric functions Homework Assignment: Transformations of f(x)...
32. Graph the following functions over 2 CYCLES Label the aves [C, 20m] a) y- sinx+60)-3 Amplitude, Maximum Minimum Period (one cycle). Vertical Translation b) y-3 sin [20x-30]-2 Period (one cycle) Amplitude, -Phase shift Maximum- Vertical Translation Minimum
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
15. The graph of which trigonometric function(s) include the point (0,2)? Select all that apply. (3 points) y = cos x + 1 y = 2 cos x y = sin x + 1 y = tan x + 1 f(x) = sin(x+y)+1 16. The data in the table represents the average number of daylight hours each month in Springfield in 2015, rounded to the nearest quarter-hour. (4 points) Month Hours January 9.5 February 10.5 March 12 April 13.25 May...
Given The partial graph of the cosine function below has a minimum post -2 nd a maximum point at C ) as shown below. The equation of the function can be expressed in the form acos -c))+d. ...c.d w . a) Draw the midline on the graph. b) What is the amplitude of the graph? c) What is the period of the graph? d) What is the value of b in the above equation? e) What is the phase shift...
Question 1. Consider these real-valued functions of two variables TVIn (r2y2) f (x, y)- 9(r,)2 2+4 (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: z0 0, 20 2, 204 (Note: Use set notation, and draw a single contour...
32 Find the equation of the tangent line to the graph of f(x) = x5 10 at x = 2. x3 V= Submit Answer Tries 0/99 Find the derivative of y = 7 sin x – 9 cos X. Remember to type in the parenthesis for trigonometric functions, for example, sin(x). y'(x) = Submit Answer Tries 0/99 Find the equation of the tangent line to the graph of y = 3 sin x at x = TT. y Submit Answer...
Consider the function below. y z= 2+x+ (a) Match the function with its graph (labeled A-F). (b) Match the function with its contour map (labeled 1-VI). O V VI Give reasons for your choices. Select- Also, the values of z approach 0 as we use This function is not periodic, ruling out the graphs in (b) Match the function with its contour map (labeled I-VI) II III IV V VI Give reasons for your choices. This function is not periodic,...
6. For f(x) = 2 + tan for-360° SXS 360°. (a) For what values are there asymptotes? (b) Write down (i) the period of the function; (ii) the value off (90°). (e) Solve f (x) = 0 for -360° SXS 360°. 4. Let (c) - cos (2x + 2), 0 S IS A. Sketch the curve of y=f(x) on the grid below. os | 15 1 25 35 The following graph shows the depth of water, y metres, at a...
13. Given y = -3 + 4cos (2x + 5) (a) What is the period? (b) How many cycles in 27 radians? (c) Is the curve shifted left or right? (d) Is the curve shifted up or down? 14. Given that y = 1 +2 cos(x) Fill in the chart and graph the function. Do not leave blanks in the chart; if a category does not apply, show that by an appropriate answer. To receive full credit for the graph,...
3. (16 points) (a) The graph of f(z) is given below. Using the graph, determine each of the following: i) 2-coordinate of local maxima ii) D-coordinate of local minima iii) open interval(s) on which is INCREASING between 1 = A and 2 =D iv) open interval(s) on which f is DECREASING between 2 = A and 1=D v) open interval(s) on which f is CONCAVE UP between 1 = A and z =D vi) open interval(s) on which f is...