which of the following does the function y = 2cos(3x - 4)+11 not have? a) reflection b) horizontal…

which of the following does the function y = 2cos(3x - 4)+11 not have? a) reflection b) horizontal translation c) vertical stretch d) vertical translation question 30 (1 point) the temperature each hour in elma, texas on october 1 is modelled by the equation t(h)=10cos(15h - 10)+30 where h is hour of the day with 0 meaning midnight, and t is the temperature in degrees celsius. how hot did it get in elma on october 1? a) 40° b) 30° c) 45° d) 25°
Answer
Explanation:
Question 29:
Step1: Analyze the function form
The general form of a cosine - type function is (y = A\cos(Bx - C)+D). For the function (y = 2\cos(3x - 4)+11), where (A = 2), (B = 3), (C = 4), (D = 11).
- The factor (A = 2) represents a vertical stretch.
- The term (-4) inside the cosine function ((3x-4)) represents a horizontal translation ((x\to x-\frac{C}{B}=x - \frac{4}{3})).
- The term (+ 11) represents a vertical translation ((y\to y + 11)). There is no factor that represents a reflection (such as a negative sign in front of the cosine function like (y=-A\cos(Bx - C)+D)).
Question 30:
Step1: Recall the range of the cosine function
The range of the cosine function (y=\cos(u)) is ([- 1,1]). For the function (t(h)=10\cos(15h - 10)+30), we want to find the maximum value.
Step2: Find the maximum value of the cosine - related function
When (\cos(15h - 10)=1) (the maximum value of the cosine function), we have (t(h)=10\times1 + 30). [t(h)=10 + 30=40]
Answer:
Question 29: a) reflection Question 30: a) (40^{\circ})