I don't know what to write for question b and c.
1 a)Determine the values of x for which the function f(x) = 3/(√x^2+3x-4) is continuous.
Values of x are -4 and 1.
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b) What does your answer in part a. represent?
c) Why is it important in determining the continuity of the function?
a) correct
b) on your graph, x = -4 and x = 1 are vertical asymptotes.
c) causes all kinds of headaches in such calculations as finding definite integrals, or even just making a sketch of the graph
To answer question b and c, let's first review the concept of continuity of a function.
A function is said to be continuous at a point x if the function is defined at that point, the left-hand limit and right-hand limit at that point exist, and the value of the function at that point matches the value of the limits. In other words, a function is continuous when there are no breaks, jumps, or holes in its graph.
Now, to answer question b:
The values -4 and 1, which were found in part a, represent the values of x for which the function f(x) = 3/(√x^2+3x-4) is continuous.
And for question c:
Determining the values of x for which a function is continuous is important because it helps us understand the behavior of the function and identify any possible points of discontinuity. Knowing these values allows us to define the domain of the function, ensuring that we avoid any problematic values that might cause the function to be undefined or discontinuous. This information is crucial for analyzing the properties of the function, such as differentiability or integrability, and for making predictions or solving problems involving the function.