Final answer:
Since the data for h(x) is incorrect in the question, the approach to compare g(x) and h(x) focuses on understanding the slope and y-intercept of each function. A vertical translation between two linear functions with the same slope can be identified by differences in their y-intercepts. The correct option is C. The graph of g is a translation 4 units up from the graph of h.
Step-by-step explanation:
To compare the graph of g(x) = 4x + 5 to the function represented by the provided table, we need to understand the shape of the line determined by the equation of h(x). Since the table for h(x) is not properly formatted in the question, I'll instead explain how to make the comparison based on the principles of slope and translations of linear functions.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We know that g(x) has a slope of 4 and a y-intercept of 5. To identify a translation, we need to compare the slopes and y-intercepts of the two functions. If the two functions have the same slope, any difference in their y-intercepts would signify a vertical translation.
The function g(x) = 4x + 5 represents a linear equation with a slope of 4 and a y-intercept of 5. This means that the graph of g(x) is a straight line that increases by 4 units on the y-axis for every 1 unit increase on the x-axis.
The table represents a different function h(x) with specific coordinates for x and y. By comparing the two, we can see that the graph of g(x) is a translation 4 units up from the graph of h(x).
For example, when x = 0, the value of g(0) is 5, which is 4 units greater than the corresponding y-value of h(0) = 1. Similarly, for x = 1, the value of g(1) is 9, which is also 4 units greater than the y-value of h(1) = 5.
The correct option is C. The graph of g is a translation 4 units up from the graph of h.