Question

given the graph of f(x) below. evaluate each of the following

1. evaluate each 2. write as coordinate point

a) ** f(2) =
b) ** f(x)=2
x=
c) ** f(x)=4
x=
this graph shows the populations of baltimore and cleveland in the 20th century. b(t) is the population of baltimore in year t, c(t) is the population of cleveland in year t.

1. estimate b(1930) and explain what it means in this situation.
2. stretch: were the two cities populations ever the same? if so, when?

Explanation:

Step1: Evaluate f(2)

Locate x = 2 on the x - axis of the first graph. Then find the corresponding y - value on the graph of y = f(x). The graph of y = f(x) has a y - value of 0 when x = 2.

Step2: Write as coordinate point

A coordinate point is of the form (x,y). Since x = 2 and y = 0, the coordinate point is (2,0).

Step3: Solve f(x)=2

Locate y = 2 on the y - axis of the first graph. Then find the x - values where the graph of y = f(x) intersects y = 2. The graph intersects y = 2 at x=-1 and x = 4.

Step4: Write as coordinate points

For x=-1, the coordinate point is (-1,2) and for x = 4, the coordinate point is (4,2).

Step5: Solve f(x)=4

Locate y = 4 on the y - axis of the first graph. Then find the x - values where the graph of y = f(x) intersects y = 4. The graph intersects y = 4 at x=-2.

Step6: Write as coordinate point

The coordinate point is (-2,4).

Step7: Estimate B(1930) for the second graph

Locate the year 1930 on the x - axis of the second graph. Then find the corresponding y - value on the graph of B(t). By looking at the graph, B(1930) is approximately 700000. It means that the population of Baltimore in the year 1930 was approximately 700000.

Step8: Check if the populations were the same

Look for the x - values (years) where the graphs of B(t) and C(t) intersect on the second graph. The graphs of B(t) and C(t) intersect around 1910. So the populations of Baltimore and Cleveland were the same around 1910.

Answer:

a) f(2)=0, (2,0)
b) x=-1,4; (-1,2),(4,2)
c) x=-2; (-2,4)

1. B(1930)≈700000; It means the population of Baltimore in 1930 was about 700000.
2. Yes, around 1910.