- #1
scientific1
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Homework Statement
sketching
Homework Equations
How to sketch H(sin(x)) if H(x) is a step function
How would you start ?!
scientific1 said:that was a question on an old exam! nothing more.
the step is assumed
H(x) = 1 if x>0
H(x) = 0 if x<0
The best way to start sketching H(sin(x)) is by first understanding the basic shape and properties of the parent function, which in this case is H(x) = sin(x). This will give you a general idea of how the graph should look like.
The key points of the graph can be determined by plugging in specific values of x into the function, such as x = 0, π/2, π, 3π/2, etc. These values will correspond to the x-intercepts, maxima, and minima of the graph.
You can use transformations, such as vertical and horizontal shifts, reflections, and stretches, to sketch H(sin(x)). These transformations will affect the shape and position of the graph, so it's important to understand how they work.
The amplitude of the function, which is the distance from the x-axis to the highest or lowest point on the graph, will determine the vertical scale of the graph. The period, which is the distance between two consecutive peaks or troughs, will determine the horizontal scale of the graph.
You can use a graphing calculator or online graphing tool to check your sketch of H(sin(x)). Simply plug in the function and compare your sketch to the actual graph. You can also check if your key points and transformations are accurate.