Question

The graph below shows the lines f(x)=1.1x+2.2 and g(x)=1.9x-0.75

. One combination of input and output values will satisfy both functions. How do you know this? Use the graph to estimate this combination of values. Then create a table of values for each function and use it to justify your answer.

Answer 1

In the figure attached, the lines are shown.

There is a combination of input and output that satisfy both functions because both lines share a common point, that is, at that point values of f(x) and g(x) are equal. This point is (3.688, 6.256)

Table of values:

x f(x) g(x)

0 1.1(0)+2.2 = 2.2 1.9(0)-0.75 = -0.75

1 1.1(1)+2.2 = 3.3 1.9(1)-0.75 = 1.15

2 1.1(2)+2.2 = 4.4 1.9(2)-0.75 = 3.05

3 1.1(3)+2.2 = 5.5 1.9(3)-0.75 = 4.95

3.688 1.1(3.688)+2.2 = 6.256 1.9(3.688)-0.75 = 6.256

4 1.1(4)+2.2 = 6.6 1.9(4)-0.75 = 6.85