y=cos(2(x-30 degree)+1) is a funstion right?is it?
how about 2^x-4?
Yes, both y = cos(2(x-30°)+1) and 2^x - 4 are considered as functions.
To determine if a given equation represents a function, you need to check if it passes the Vertical Line Test. The Vertical Line Test states that a graph represents a function if and only if a vertical line intersects the graph at most once.
For the equation y = cos(2(x-30°)+1):
1. We know that cos(x) is a periodic function with a period of 2π.
2. The "2(x-30°)" inside the cosine function stretches the graph horizontally, making each period take half the usual length.
3. The "+1" shifts the graph upward by 1 unit.
Since each vertical line intersects the graph at most once, this equation represents a function.
For the equation 2^x - 4:
1. We have an exponential function where the base is 2 and the exponent is x.
2. The "-4" subtracts 4 from the output value.
Again, since each vertical line intersects the graph at most once, this equation also represents a function.