The functions f(x) = -2x + 2 and g(x) = (1/3)^x are shown in the graph.

What are the solutions to -2x + 2 = (1/3)^x + 1?
(Multiple choice)

A. -1
B. 0
C. 2
D. 3
E. 4

Option a: -1

Option b: 0

Explanation:

The function and

To determine the solution of and solving the expression using lambert's form, we get the solution

Hence, the solution to the functions and are -1 and 0.

Also, by looking at the graph, we can see that, the graphs f(x) and g(x) intersect at the points and .

Hence, the solution to is -1 and0.

Thus, Option a and Option b are the correct answers.

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."