Question

Hillary observes that if f(x) = 2x, then the graphs of 2f(x) and f(x) + 1 both have a y-intercept of 2.

Answer 1

Answer: No. They transform the point (0, f(0)) in the same way but not the other points on the graph.

Step-by-step explanation:

Given:

f(x) = 2x

Let the coordinate of the point be ( a , b )

Therefore :

2(fx) means that the value of y will be multiplied by 2 , that is

2f(x) = ( a , 2b)

This means that the graph of the function is stretch to the y - axis by 2

f(x) + 1 means that 1 will be added to the value of y , that is

This means that the graph of the function move upward to the y - axis by 1

f(x) + 1 = (a , b + 1)

This shows that they transform the point (0, f(0)) in the same way.

Take for example the graph of 3f(x) and the graph of f(x) - 5

The graph of 3f(x) stretch to the y - axis by 3 when the graph of f(x) - 5 move downward to the y axis by 5 .

We can therefore conclude that

if f(x) = 2x, then the graphs of 2f(x) and f(x) + 1 both have a y-intercept of 2.They transform the point (0, f(0)) in the same way but not the other points on the graph.