Answer:
7. Function A has the greater initial value.
9. Function A is nonlinear.
Function B is linear.
Step-by-step explanation:
7. The initial value of a function is the same as the y-intercept, or the value of y when x equals 0. For function A, the y-intercept is 4.
Function B is written in slope-intercept form, y = mx + b, where b represents the y-intercept. So, the y-intercept of function B is 3.
Finally, let's compare the y-intercepts of both functions. 4 is greater than 3, which means that Function A has the greater initial value.
9. A function is linear when the change in y over the change in x is proportional.
Function A: Let's look at the graph of Function A. It has points at (0, -1), (1, 0), and (2, 3). From point (0, -1) to point (1, 0), the value of x and the value of y both increase by 1. However, from point (1, 0) to point (2, 3), the value of x goes up by 1 but the value of y goes up by 3. Since the increase in y is not proportional, Function A is nonlinear.
Function B: Function B is written in the form y = mx, where m represents the change in y over the change in x. For this equation, m = 1. This means that every time the value of x increases by 1, the value of y increases by 1 as well. This represents a proportional relationship, so Function B is linear.
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