Question

he graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 6. Function 2 y = 2x + 7 How much more is the rate of change of function 2 than the rate of change of function 1? 1 2 3 4

Answer 1

Answer:

The answer is 2

Step-by-step explanation:

Rate of change of function is given by :

$\frac{(f(x_{2})-f(x_{1}))}{x_{2}-x_{1}}$

For function y = 6,

rate of change =  

$=\frac{(f(x_{2})-f(x_{1}))}{x_{2}-x_{1}}\\=\frac{6-6}{x_{2}-x_{1}}\\=0$

because the function is independent of x.

For function y = 2·x + 7,

rate of change =

$=\frac{(f(x_{2})-f(x_{1}))}{x_{2}-x_{1}}\\=\frac{2\cdot x_{2}+7-2\cdot x_{1}-7}{x_{2}-x_{1}}\\=\frac{2\cdot x_{2}-2\cdot x_{1}}{x_{2}-x_{1}}\\=\frac{2\cdot (x_{2}-x_{1})}{x_{2}-x_{1}}\\=2$

So, the rate of change of 2 is greater than rate of change of function 1 by 2 - 0 = 2.