Question

Juan Carlos graphs the functions f(x)=5x-2 and g(x)=-5x+2

Part A
At what point will the graphs of these functions intersect?

Part B
what is the solution to the equation f(x)=g(x) ?

Answer 1

Two linear functions that have different slopes will give graphs that intersect at a point known as the solution to the two functions

Part A: The point at which the graphs of the functions intersect is (0.4, 1)

Part B: The solution to the equation f(x) = g(x) is f(x) = g(x) = 1 when x = 0.1

The reason the above values are correct are as follows:

The functions graphed by Juan Carlos are f(x) = 5x - 2, and g(x) = -5·x + 2

Part A:

The point on the graph the functions intersect is given by the point where the values of the function are equal as follows;

At the intersection point, f(x) = g(x), therefore;

At the intersection point, 5x - 2 = -5·x + 2

5x - 2 = -5·x + 2

5x + 5·x = 2 + 2

10·x = 4

$x = \dfrac{4}{10} = \dfrac{2}{5} = 0.4$

x = 0.4

The value of the function at the intersection point f(0.4) = 5×0.2 - 2 = 1

f(0.4) = 1

The coordinates of the intersection point on the graph, (f(x), x) is (0.4, 1)

Part B:

The solution of the equation f(x) = g(x) as found above, is given by the x-value at the point of intersection, which is f(x) = g(x) = 1 when x = 0.4

Learn more about the intersection of line graphs here:

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