FUNCTIONS AND GRAPHS VI
The afine function
A constant function.
y = 7/2
it is said to be constant because any value of x always corresponds to the same value 7/2.
1.- Move the point, change the scale and see that the points which fulfil this condition lie on the straight line.
The constant function.
y = k
2.- Represent the functions: y = 3 ; y = 5 ; y = ¼ ; y = -2 ; ... and answer the following questions in your book.
Which straight line represents the function y = 0?
What characteristics do all the straight lines which represent the constant functions have? How do these lines compare to each other? At what point do they cut the ordinate axis?
The function plus 3.
3.- Observe the points of the function plus 3, that is to say:
y = x + 3
Draw this graph in your work book.
Comparison with the identity function:
y = x
y = x + 3
4.- Observe the graphs of the identity function and the function plus 3.
How do the straight lines represented by these two functions resemble each other?
Where does the graph of the function plus 3 cut the axes?
What would the graphs be like for the functions plus one, plus ¾, minus five, etc.
The function plus k.
y = x + k
5.- Represent various functions for different values of k.
How are the graphs of these functions like with respect to each other?
What are the coordinates of the points of intersection with the axes?
The function double plus three:
y = 2 * x + 3
6.- Compare this function with the linear function
y = 2 * x.
