What is the domain, range, and period of y= sin x + 1
What is the domain, range, and period of y= -cos x
Can someone please help?
domain of sin(x) and cos(x) is all reals
period of sin(x) and cos(x) is 2pi
range of sin(x) and cos(x) is [-1,1]
sin(x)+1 is just like sin(x) but raised +1 on y, so all that's changed is the range: [0,2]
-cos(x) is just cos(x) reflected in the x-axis, so nothing is changed.
thank you!
Of course! I'd be happy to help. Let's start with the first function, y = sin(x) + 1.
The domain of a function represents all the possible inputs, or x-values, for which the function is defined. Since the sine function, sin(x), is defined for all real numbers, the domain of y = sin(x) + 1 is also all real numbers.
The range of a function represents all the possible outputs, or y-values, that the function can produce. Adding 1 to the sine function does not change its range, so the range of y = sin(x) + 1 is from 0 + 1 = 1 to 2 + 1 = 2. In other words, the range is [1, 2].
Now let's move on to the second function, y = -cos(x).
Similar to the previous function, the domain of y = -cos(x) is all real numbers because the cosine function, cos(x), is defined for all real numbers.
The range of the cosine function is between -1 and 1. Negating the cosine function does not change its range, so the range of y = -cos(x) is also between -1 and 1, but in this case, it is [-1, 1].
Finally, the period of a function represents the horizontal distance between two consecutive identical points on the graph. For the cosine function, the period is 2π, which means it repeats every 2π units. Negating the cosine function does not change its period, so the period of y = -cos(x) remains 2π.
I hope this explanation helps! Let me know if you have any further questions.