Question

Given g(x) = 5x – 7, what function h(x) would represent a upward shift by four units?

A) h(x) = x – 7
B) h(x) = 9x – 7
C) h(x) = 5x – 3
D) h(x) = 5x – 11

Answer 1

To create a function h(x) that represents a four-unit upward shift from g(x) = 5x - 7, we add 4 to the constant term. The correct function is h(x) = 5x - 3, which is answer C).

Step-by-step explanation:

The function g(x) = 5x – 7 represents a linear function. To represent an upward shift by four units of this function, you would add 4 to the entire function, affecting the y-intercept but not the slope. Therefore, the function h(x) that represents an upward shift by four units of function g(x) is h(x) = 5x – 3, because (-7) + 4 = (-3). The new function simply increases the y-values of the original function g(x) by 4 for each corresponding x-value, without changing the shape or orientation of the graph of g(x). Thus, the correct answer is C) h(x) = 5x – 3.