Answer:
Yes, the relation is a function.
Step-by-step explanation:
Given:
The equation that represents the cost of riding a cab is given as:
[tex]y=0.75x+3[/tex]
Where, 'x' is the number of miles traveled and 'y' is the the total cost of the trip.
The above equation represents a line as it is of the form [tex]y=mx+b[/tex] which represents a line with constant slope.
Now, in order to plot this equation, we need at least two points.
Now, let [tex]x =0[/tex], then
[tex]y=0.75(0)+3=3[/tex]. So, (0, 3) is a point on the line.
Let [tex]x =1[/tex], then
[tex]y=0.75(1)+3=3.75[/tex]. So, (1, 3.75) is a point on the line.
Plot these two points on a graph and draw a line passing through these two points.
Now, for a relation to be a function, it should pass the vertical line test.
According to vertical line test, vertical lines passing through the graph must cut the graph at only 1 point for the graph to represent a function.
Here, we observe that vertical lines passing through the line will intersect the line only at one point. So, it represent a function.
