Final answer:
The new function f(x) = 7x - 4 shifted 5 units down means that the graph of the function will be moved downwards by 5 units compared to the original graph of f(x) = 7x - 4.
Step-by-step explanation:
The new function f(x) = 7x - 4 shifted 5 units down means that the graph of the function will be moved downwards by 5 units compared to the original graph of f(x) = 7x - 4.
To visualize this shift, you can think of taking each point on the original graph and moving it 5 units downwards. For example, if the original graph had a point at (2, 10), after the shift, this point would be located at (2, 5).
So, the new function would be f(x) = 7x - 4 - 5, which simplifies to f(x) = 7x - 9.
The student is asking about a transformation of the function f(x) = 7x - 4. When a function undergoes a shift, it is translated vertically or horizontally without changing its shape. The question specifically describes a vertical shift of 5 units downwards. To apply this transformation, you subtract 5 from the original function, resulting in the new function g(x) = f(x) - 5 = 7x - 4 - 5. Therefore, the transformed function is g(x) = 7x - 9.