Question

Describe the transformations that would be preformed on f(x) to obtain the function.

Answer 1

The equation provided is y = f(5x) + 1. This equation represents a function, where the value of y is dependent on the value of 5x.

To evaluate this equation, you would substitute a value for x, then perform the necessary calculations to find the corresponding value of y.

For example, let's say we want to find the value of y when x = 2.

1. Substitute the value of x into the equation: y = f(5(2)) + 1.

2. Simplify the equation: y = f(10) + 1.

3. Now, the value of y depends on the function f. If the function f is defined or given, you would substitute 10 into the function and then add 1 to the result.

4. However, since the equation does not specify the function f, we cannot determine the exact value of y. We can only evaluate it further if we have additional information about the function f.

In summary, the equation y = f(5x) + 1 represents a function where the value of y depends on the value of 5x. To find the value of y, substitute a value for x and evaluate the equation accordingly. However, without information about the specific function f, we cannot determine the exact value of y.

Explanation:

Answer 2

A horizontal compression by a factor of 1/5, followed by a vertical shift upward by 1 unit.

Explanation:

To obtain the function y = f(5x) + 1 from the original function f(x), the following transformations need to be applied:

1. Horizontal compression (scale factor 1/5)

When the input of a function is multiplied by a positive constant "b", where b > 1, it results in a horizontal compression of the function by a scale factor of 1/b.

Therefore, the graph of f(5x) is a horizontal compression of the graph of the original function f(x) by a scale factor of 1/5.

2. Vertical shift (one unit upward)

When we add a constant "c" to a function, it corresponds to a vertical upward shift of the graph.

Therefore, in the equation y = f(5x) + 1, the addition of one represents a vertical shift of one unit upward.

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Conclusion

In summary, the series of transformations applied to f(x) to obtain y = f(5x) + 1 involves a horizontal compression by a factor of 1/5 followed by a vertical shift upward by 1 unit.