See attachment for the graph of the piecewise function h(x)
<h3>How to plot the function?</h3>The function is given as:
h(x) = | -4, x < 3
| x + 5, x >= 3
The above function is a piecewise function.
It has 2 separate functions at two domains
This means that we plot the sub-functions in the piecewise function at their respective domain
See attachment for the graph of the piecewise function h(x)
Read more about piecewise function at:
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Answer:
Unfortunately, your answer is not right.
Step-by-step explanation:
The functions whose graphs do not have asymptotes are the power and the root.
The power function has no asymptote, its domain and rank are all the real.
To verify that the power function does not have an asymptote, let us make the following analysis:
The function , when x approaches infinity, where does y tend? Of course it tends to infinity as well, therefore it has no horizontal asymptotes (and neither vertical nor oblique)
With respect to the function we can verify that if it has asymptote horizontal in y = 0. Since when x approaches infinity the function is closer to the value 0.
For example: 1/2 = 0.5; 1/1000 = 0.001; 1/100000 = 0.00001 and so on. As "x" grows "y" approaches zero
Also, when x approaches 0, the function approaches infinity, in other words, when x tends to 0 y tends to infinity. For example: 1 / 0.5 = 2; 1 / 0.1 = 10; 1 / 0.01 = 100 and so on. This means that the function also has an asymptote at x = 0