The following graph models the braking distance B in feet as

The following graph models the braking distance, B, (in feet) as a function of the speed a vehicle (in miles per hour). Use the graph to answer the questions that follow Explain why the graph represents a function Write the function notation for the situation Use the graph to solve B(s) = 50 State the contextual meaning of the of part \'c\' in a complete sentence.

Solution

a) No two x values have same y value.Further with vertical line drawn , it cuts the graph

at not more than 1 place

b) we would look for some points from the graph to find the function .

we take two points from graph ( x , y ) = ( 30, 40) ; (40 , 70) ( these are approximate points)

we check if its a parabolic function :y2/y1 = (x2/x1)^2 ; 70/40 = ( 40/30)^2 ; 1.75 = 1.77

They are approximately same on LHS and RHS

Now graph reprsents parabolic function :B(s) = ks^2

y2/y1 = (x2/x1)^2 ; 70/40 = ( 40/30)^2 ; 1.75 = 1.77

function notation : B(s) = ks^2   where k is a constant

c) B(s) = 50

draw a horizontal line and check where it intersects the graph.

s = 35 mph

d) At a speed of s = 35 mph , braking distance B(s) = 50 feet