Question

x | h(x)0 | -61 | -6⅔2 | -7⅓3 | -8Which function decreases faster?A) hB) pC) The functions decrease at the same rate

Answer 1

Two coordinates of the graph of function p is,

(x1, y1)=(0,-7)

(x2,y2)=(-6,-3)

Now, the slope of the graph is,

`\begin{gathered} (dy)/(dx)=(y_2-y_1)/(x_2-x_1) \\ =(-3-(-7))/(-6-0) \\ =(-3+7)/(-6) \\ =(4)/(-6) \\ =(-2)/(3) \end{gathered}`

Consider two points of the function h(x).

(x1,y1)=(0,-6).

(x2,y2)=(3,-8).

The slope of graph of function h(x) is,

`\begin{gathered} \text{Slope=}(dy)/(dx)=(y_2-y_1)/(x_2-x_1) \\ =(-8-(-6))/(3-0) \\ =(-8+6)/(3) \\ =(-2)/(3) \end{gathered}`

The slopes of the graphs of functions gives the rate of change of the function.

Since the slopes of graphs of both functions h(x) and p(x) is -2/3, the functions decrease at a constant rate.

Therefore, option C is correct.