which statement about linear functions are true
A)linear functions grow by equal factors over equal intervals
B)linear functions grow by equal differences over equal intervals
C)linear functions grow by equal differences over unequal intervals
D)linear functions grow by unequal factors over equal intervals
I think the answer was A, is this correct? If not can you help explain this.
Thanks for your help.
Better check B.
It's the differences that are constant, not the ratios. A gives an exponential function.
Consider y = 2^x
when x grows by 1, y doubles.
But, if y = mx+b (a linear function)
when x grows by 1, y grows by m, and the difference is constant over equal intervals.
The correct statement about linear functions out of the options given is B) linear functions grow by equal differences over equal intervals.
To explain this concept, let's first understand what a linear function is. A linear function is a mathematical relationship between two variables, x and y, that can be represented by a straight line on a graph. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept.
In the context of the question, we are considering the growth or change of a linear function over intervals. The key idea is that the change in the value of y (vertical change) is determined by the change in the value of x (horizontal change) with a constant rate or difference. This is called the slope of the line.
Option B states that linear functions grow by equal differences over equal intervals. This means that the change in the value of y is the same over equal intervals of x. In other words, for every unit increase in x, the value of y increases by the same amount.
Option A, on the other hand, states that linear functions grow by equal factors over equal intervals. This is not correct because linear functions do not have exponential growth. It is the property of exponential functions to grow by equal factors over equal intervals.
Option C states that linear functions grow by equal differences over unequal intervals. This is also not true because if the intervals of x are unequal, the rate of change or slope of the linear function may vary.
Option D states that linear functions grow by unequal factors over equal intervals. This is not true for linear functions because their growth is constant and determined by a fixed slope.
Therefore, the correct statement is B) linear functions grow by equal differences over equal intervals.