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Given f(x) = 2 - 5, create a function g(2) that is steeper and shifts down 4 units on the y-axis.

User Denhackl
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Final answer:

To create a steeper function that is shifted down by 4 units, you can define a new function g(x) with a steeper slope and a downward shift, such as g(x) = 2x - 4.

Step-by-step explanation:

The student appears to have made a typo in describing the original function as f(x) = 2 - 5, which simplifies to f(x) = -3, a constant function. However, if we proceed with the intention of creating a steeper line that is shifted down, we can manipulate this constant function.

To create a function g(x) that is steeper than f(x), we can multiply the x term by a constant greater than 1 since the original function does not have an x term. For instance, g(x) = kx where k > 1. Additionally, to shift the function down 4 units, we subtract 4 from the constant term, resulting in g(x) = kx - 4. Assuming k is a positive number, k could be greater than 1, for example, 2, to increase the steepness of the slope. Therefore, a suitable function might look like g(x) = 2x - 4.

User Wickdninja
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