Question

How would the graph of the function F(x) = -x - 5 be affected if the function were to change to g(x) = 6x + 1? Please provide a detailed explanation of how the graph of g(x) differs from that of F(x).

Answer 1

The graph of g(x) has a positive slope and a higher y-intercept compared to the graph of F(x), making it steeper and shifted upward.

Step-by-step explanation:

The function F(x) = -x - 5 represents a linear equation in slope-intercept form, where the slope is -1 and the y-intercept is -5. This means that for every 1 unit increase in x, the value of y decreases by 1. The graph of F(x) is a straight line with a negative slope and y-intercept at -5.

On the other hand, the function g(x) = 6x + 1 represents a linear equation with a slope of 6 and a y-intercept at 1. This means that for every 1 unit increase in x, the value of y increases by 6. The graph of g(x) is a straight line with a positive slope and a y-intercept at 1.

Therefore, the graph of g(x) is steeper than the graph of F(x) and is shifted upward on the y-axis compared to the graph of F(x).