PLZZZZ HELP
Recall that a radical function can be expressed as f(x)= a*sqrt( x - h) + k. How do the values of A, H, and K, affect the domain and range of a radical function? How is this similar to other functions you have learned about (such as linear, quadratic, or exponential functions)? How is it different? Give examples and justify your ideas.
gee, impatient much?
duplicate posts are just annoying. Makes me wish I hadn't helped already.
Thanks, can reply on the last one again pretty plz
Thanks for the help
To understand how the values of A, H, and K affect the domain and range of a radical function, let's break it down step-by-step.
1. A: The value of A determines the vertical stretch or compression of the graph. If A is positive, it stretches the graph vertically, and if it is negative, it compresses the graph vertically. The absolute value of A also determines how steep or flat the graph becomes.
2. H: The value of H represents the horizontal shift of the graph. It tells us how much the graph is shifted horizontally. If H is positive, the graph moves to the right, and if it is negative, the graph moves to the left.
3. K: The value of K represents the vertical shift of the graph. It tells us how much the graph is shifted vertically. If K is positive, the graph moves upward, and if it is negative, the graph moves downward.
Now, let's discuss how these factors relate to the domain and range of the radical function.
1. Domain: The domain of a radical function is the set of all possible x-values for which the function is defined. In this case, since we have a square root function, the radicand (x-h) must be non-negative. Therefore, for the function to be defined, x - h ≥ 0. Solving this inequality, we find that x ≥ h. So, the domain of the radical function is all x-values greater than or equal to h.
2. Range: The range of a radical function is the set of all possible y-values or output values. Since the square root function can take any non-negative value, the range of the radical function is all real numbers greater than or equal to K.
Now, let's discuss the similarities and differences between the effects of A, H, and K in radical functions compared to other functions.
Similarities:
1. Like linear, quadratic, and exponential functions, the values of A, H, and K influence the transformation of the graph of the function.
2. Like other functions, changing the value of A affects the vertical stretch or compression of the graph.
3. Like other functions, changing the value of H affects the horizontal shift of the graph.
4. Like other functions, changing the value of K affects the vertical shift of the graph.
Differences:
1. Unlike linear and quadratic functions, the values of A, H, and K in a radical function do not affect the shape of the graph.
2. Unlike exponential functions, changing the value of A in a radical function does not impact the growth or decay rate; it only affects the vertical stretch or compression.
Example 1:
Consider the function f(x) = 2*sqrt(x - 3) - 1.
The value of A is 2, indicating a vertical stretch of the graph.
The value of H is 3, indicating a horizontal shift to the right by 3 units.
The value of K is -1, indicating a vertical shift down by 1 unit.
Example 2:
Now consider the function f(x) = -sqrt(x + 1) + 4.
The value of A is -1, indicating a vertical compression of the graph.
The value of H is -1, indicating a horizontal shift to the left by 1 unit.
The value of K is 4, indicating a vertical shift up by 4 units.
These examples illustrate how changes in A, H, and K affect the shape, position, and range of the radical function.
Remember, understanding how A, H, and K influence the domain, range, and transformation of a radical function will help you analyze and graph various types of radical functions.