Question

Let f(x) = x+3 . Graph g(x) = f(5x)

Answer 1

To graph g(x) = f(5x) when f(x) = x + 3, scale the x-axis of the graph of f(x) by 1/5 and label the axes with the maximum values for clarity.

Step-by-step explanation:

The student's question revolves around composing the function g(x) given that g(x) = f(5x) and f(x) = x + 3. To graph g(x), we follow the steps:

1. Identify the original function f(x), which in this case is a linear function f(x) = x + 3.
2. Understand the transformation applied to f(x) to get g(x), which is multiplying the input by 5. This means we are effectively scaling the x-axis by a factor of 1/5.
3. Graph the original function f(x) from 0 ≤ x ≤ 20.
4. Transform this graph to get g(x) by scaling the x-values. For each value of x in f(x), divide the x-coordinate by 5 to achieve the horizontal scaling.
5. Label the graph with f(x) and x. Scale the x and y axes with the maximum x and y values.

Scaling the x-values in this manner creates a steeper graph when compared to f(x), because for every unit increase in x, the change in the function value happens five times faster. However, the y-intercept remains the same since f(0) is unchanged in the transformation.