Sure, I can help you.
Part A:
To find the slope of a function from a table, we take any two points and calculate the change in the y-values over the change in the x-values. For function f(x), we can take the points (-1, -12) and (1, 0) and set them into the formula for slope (change in y / change in x). Thus, it will look like this:
Slope of f(x) = (0 - (-12)) / (1 - (-1)) = 12/2 = 6.
So, the slope of f(x) is 6.
On the other hand, slope for the function g(x) is given directly from the equation g(x) = 2x + 6. The number in front of x (coefficient of x) in any linear equation represents the slope. Thus, the slope of g(x) is 2.
Now, for creating the sentence to compare we can use the obtained values. Here it is:
"The slope of f(x) is 6.0, while the slope of g(x) is 2."
Part B:
The y-intercept of a function is the value of y when x = 0. For the function f(x) using the provided table, we see that when x = 0, f(x) = -6. So, the y-intercept of f(x) is -6.
For the function g(x), the y-intercept comes directly from the equation provided: g(x) = 2x + 6. The y-intercept is the constant term, which in this case is 6.
Therefore, g(x) has a greater y-intercept (6) compared to f(x) (-6), because 6 is larger than -6.
Justification:
"Function g(x) has a greater y-intercept. This is because the y-intercept of g(x) is 6, while the y-intercept of f(x) is -6."
So, to summarize, function f(x) has a greater slope but function g(x) has a greater y-intercept.