![]() 2 pi over 6 pi minus 2 pi is negative pi over 6 and we have to take the mid line of 3 and then we're at the mac. If we shrink it by 3, we'll be at pi over 6 p, and if we leave it at 3, we'll be at negative pi. There will be a horizontal shrink, a vertical stretch and a shift up 3. Pi over 3 will take that to go left pi over 3 and then up three the next quarter, point which would be a maximum, which is at pi over 21. Where would that be located? The face shift will affect this and the vertical shift. If we think about the original graph of sin 1 period, the quarter point starts at 0, this is good. When you factor out the 3 out, you're left with pi over 3. Since we have a horizontal shrink of 3, the period of sin is 2 pi over 3. If there is a shift up 3, then the whole mid line has gone up 3 and if the amplitude is 2, then we know it's going up and down from the mid line, so 3 plus 2 is 53. Type exact answers using as needed_ Use integers or fractions for any numbers in the expressions_ Quarter points of (0,0) (1,0) (2x,0) y = sinx Quarter points of y=2sin (3x + n) + 3 (Simplify your answers. (Simplify your answer: Type an exact answer using as needed_ Use integers or fractions for any numbers in the expression ) Use the coordinates of the five quarter points of y = sin x to determine the corresponding quarter points on the graph of y = 2 sin (3x + x) + 3. The phase shift ofy = 2 sin (3x+ x) - 3 is (Simplify your answer: Type an exact answer using as needed: Use integers or fractions for any numbers in the expression ) Use integers or fractions for any numbers in the expression ) The range of y = 2 sin (3x + x) + 3 is ]- (Simplify your answer: Type your answer in interval notation. Hand drawn sketch like in Ch 5.3 Example 4 to help show your work.ĭo not use a calculator to just write the answer.ģ months ago Use the 5 step process given in Section 5.5 to find the 5 keyĭetermine the amplitude range period_ and phase shift and then sketch the graph of the function using the quarter points_ Do not use a calculator to just write the answer. Drawing sketches insure you have the correct signs forĪnswers. Sketch to show (and label) the reference angle like in Examples 7Īnd 8. Use reference angles and the 2 step process in Section 5.3 toįind the exact value of each expression. Use one of the graphing tools (Desmos or Graphmatica) graph theįunction and compare to your hand sketch. Make a hand sketch for 2 periods of your function and add it to Example 2 in section 5.6 canīe very helpful with the level of detail required. Use the 4 step process given in Section 5.6 to find and give theĪsymptotes, x-intercepts, quarter points and three-quarter pointsįor two consecutive asymptotes for graphing. ![]() Make a hand sketch for 1 period of your function and add it to Very helpful with the level of detail required. Label the steps, give necessaryįormulas, and show work for finding and reporting the amplitude, SOLVED: Use the 5 step process given in Section 5.5 to find the 5 key
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